Details

analyze1.7s (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.3s (0.2%)

Algorithm

1×

intervals

Results

1.2s	103×	body	8192	exit
82.0ms	256×	body	128	valid
8.0ms	363×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify157.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.8b

Counts

2 → 2

Compiler

Compiled 74 to 61 computations (17.6% saved)

localize60.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5893731530977871/590295810358705651712 (-.f64 7 z))
0.0b	(+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))
0.0b	(/.f64 848079078717083/1099511627776 (-.f64 3 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite173.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_1442`
44×	`add-log-exp_binary64_1481` `frac-add_binary64_1450`
31×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393`
10×	`add-exp-log_binary64_1480`
9×	`add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503`
7×	`prod-exp_binary64_1491`
5×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
4×	`associate-r_binary64_1382`
3×	`cbrt-unprod_binary64_1475`
2×	`sqrt-pow1_binary64_1460` `associate-+l+_binary64_1375` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513`
1×	`associate-r/_binary64_1384` `pow-exp_binary64_1510` `associate-l_binary64_1383` `-commutative_binary64_1373` `pow-sub_binary64_1518` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `associate-*l/_binary64_1385` `exp-sum_binary64_1488` `pow-to-exp_binary64_1511`

Counts

4 → 86

Calls

8 calls:

101.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
23.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
17.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series373.0ms (0.1%)

Counts

4 → 30

Calls

4 calls:

211.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
98.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
64.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2240 to 1860 computations (17% saved)

simplify106.0ms (0%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5257	8452

localize70.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))
0.0b	(+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))
0.0b	(/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1))
0.0b	(/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)

rewrite67.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1442`
28×	`add-sqr-sqrt_binary64_1464`
24×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481`
16×	`associate--l+_binary64_1379`
12×	`diff-log_binary64_1534` `add-cube-cbrt_binary64_1477` `distribute-lft-out--_binary64_1394`
8×	`sub-neg_binary64_1435` `difference-of-squares_binary64_1411`
4×	`associate--l-_binary64_1380` `add-cbrt-cube_binary64_1478` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `add-exp-log_binary64_1480` `flip--_binary64_1417` `pow1_binary64_1503`

Counts

4 → 100

Calls

8 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
0.0ms	(/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))

series160.0ms (0%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (-.f64 1 z) 1)
41.0ms	(-.f64 (-.f64 1 z) 1)
38.0ms	(-.f64 (-.f64 1 z) 1)
38.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 2904 to 2592 computations (10.7% saved)

simplify87.0ms (0%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5392	704

prune3.7s (0.6%)

Pruning

75 alts after pruning (73 fresh and 2 done)

	Pruned	Kept	Total
New	155	73	228
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	155	75	230

Error

0.3b

Counts

230 → 75

Compiler

Compiled 25790 to 21146 computations (18% saved)

localize121.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite156.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
12×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393`
8×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450`
4×	`add-cbrt-cube_binary64_1478` `+-commutative_binary64_1372` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `associate-+r+_binary64_1374` `add-cube-cbrt_binary64_1477`

Counts

4 → 68

Calls

8 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series866.0ms (0.1%)

Counts

4 → 47

Calls

4 calls:

218.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
217.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
216.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
214.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 18600 to 15600 computations (16.1% saved)

simplify100.0ms (0%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5026	2557

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
0.0b	(/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))
0.0b	(pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))
0.0b	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))
0.2b	(*.f64 PI.f64 z)
0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
14×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478`
11×	`pow1_binary64_1503`
9×	`times-frac_binary64_1448`
8×	`prod-exp_binary64_1491`
7×	`associate-r_binary64_1382`
4×	`cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `add-log-exp_binary64_1481`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `pow-prod-down_binary64_1513`
2×	`sqrt-pow1_binary64_1460` `*-commutative_binary64_1373`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `div-inv_binary64_1439` `clear-num_binary64_1441` `pow-sub_binary64_1518` `frac-2neg_binary64_1453` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `associate-l/_binary64_1385` `div-exp_binary64_1493` `exp-sum_binary64_1488` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 77

Calls

8 calls:

17.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(*.f64 PI.f64 z)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))

series179.0ms (0%)

Counts

4 → 9

Calls

4 calls:

111.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
39.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
29.0ms	(*.f64 PI.f64 z)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 607 to 501 computations (17.5% saved)

simplify112.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4918	1430
1	4918	1430

localize69.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5893731530977871/590295810358705651712 (+.f64 (-.f64 (-.f64 1 z) 1) 7))
0.0b	(+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))
0.0b	(/.f64 5950736089418501/8796093022208 (+.f64 (-.f64 (-.f64 1 z) 1) 1))
0.0b	(/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)
4.4b	(-.f64 (-.f64 1 z) 1)

rewrite66.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1442`
28×	`add-sqr-sqrt_binary64_1464`
24×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481`
16×	`associate--l+_binary64_1379`
12×	`diff-log_binary64_1534` `add-cube-cbrt_binary64_1477` `distribute-lft-out--_binary64_1394`
8×	`sub-neg_binary64_1435` `difference-of-squares_binary64_1411`
4×	`associate--l-_binary64_1380` `add-cbrt-cube_binary64_1478` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `add-exp-log_binary64_1480` `flip--_binary64_1417` `pow1_binary64_1503`

Counts

4 → 100

Calls

8 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
0.0ms	(/.f64 848079078717083/1099511627776 (+.f64 (-.f64 (-.f64 1 z) 1) 3))

series160.0ms (0%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 2832 to 2520 computations (11% saved)

simplify86.0ms (0%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5392	704

localize102.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite140.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
12×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393`
8×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450`
4×	`add-cbrt-cube_binary64_1478` `+-commutative_binary64_1372` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `associate-+r+_binary64_1374` `add-cube-cbrt_binary64_1477`

Counts

4 → 68

Calls

8 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series511.0ms (0.1%)

Counts

4 → 47

Calls

4 calls:

128.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
128.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
128.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
127.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 10056 to 8352 computations (16.9% saved)

simplify93.0ms (0%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5026	2557

localize120.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
1.0b	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite449.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

636×	`frac-times_binary64_1452`
384×	`associate-*l/_binary64_1385`
367×	`flip3--_binary64_1446` `flip--_binary64_1417`
234×	`associate-*r/_binary64_1384`
141×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
64×	`frac-add_binary64_1450`
50×	`pow1_binary64_1503`
47×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
33×	`pow-prod-down_binary64_1513`
32×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
8×	`add-cube-cbrt_binary64_1477`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
4×	`associate-l_binary64_1383`
2×	`sqrt-pow1_binary64_1460` `associate-+l+_binary64_1375` `sub-neg_binary64_1435` `*-commutative_binary64_1373` `associate-+r+_binary64_1374`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 408

Calls

8 calls:

48.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
39.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
33.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series361.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

122.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
122.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
116.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 5921 to 4855 computations (18% saved)

simplify515.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

426 → 426

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4972	43405
1	4972	43405

prune1.8min (17.8%)

Pruning

332 alts after pruning (326 fresh and 6 done)

	Pruned	Kept	Total
New	595	259	854
Fresh	1	67	68
Picked	0	0	0
Done	1	6	7
Total	597	332	929

Error

0.1b

Counts

929 → 332

Compiler

Compiled 260199 to 211966 computations (18.5% saved)

localize148.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
3.1b	(-.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (.f64 (-.f64 2 z) (-.f64 2 z))) (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))

rewrite160.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-log-exp_binary64_1481`
19×	`*-un-lft-identity_binary64_1442`
12×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
9×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393`
8×	`frac-sub_binary64_1451`
6×	`add-sqr-sqrt_binary64_1464` `frac-add_binary64_1450`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `frac-times_binary64_1452` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
3×	`+-commutative_binary64_1372` `associate-+r+_binary64_1374`
2×	`associate-r/_binary64_1384` `associate--r+_binary64_1378` `difference-of-squares_binary64_1411` `associate-l/_binary64_1385`
1×	`cancel-sign-sub-inv_binary64_1408` `times-frac_binary64_1448` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`

Counts

4 → 75

Calls

8 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
24.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
18.0ms	(-.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (.f64 (-.f64 2 z) (-.f64 2 z))) (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series796.0ms (0.1%)

Counts

4 → 41

Calls

4 calls:

216.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
215.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
214.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
149.0ms	(-.f64 (/.f64 30666706506962181608371823434969/19342813113834066795298816 (.f64 (-.f64 2 z) (-.f64 2 z))) (.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))))

Compiler

Compiled 18067 to 15161 computations (16.1% saved)

simplify77.0ms (0%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4944	3496
1	4944	3496

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
0.0b	(/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))
0.0b	(pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))
0.0b	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))
0.1b	(exp.f64 (+.f64 z -15/2))
0.2b	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite76.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-exp-log_binary64_1480`
79×	`prod-exp_binary64_1491`
41×	`add-cbrt-cube_binary64_1478`
23×	`cbrt-unprod_binary64_1475`
18×	`pow1_binary64_1503`
16×	`associate-*r/_binary64_1384`
15×	`*-un-lft-identity_binary64_1442`
14×	`associate-l_binary64_1383`
13×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
12×	`div-exp_binary64_1493`
10×	`associate-*l/_binary64_1385`
9×	`times-frac_binary64_1448` `frac-times_binary64_1452`
8×	`pow-prod-down_binary64_1513`
7×	`pow-sub_binary64_1518` `add-log-exp_binary64_1481`
6×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
5×	`associate-r_binary64_1382` `pow-exp_binary64_1510` `pow-to-exp_binary64_1511`
4×	`cbrt-undiv_binary64_1476` `exp-prod_binary64_1494` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416`
2×	`sqrt-pow1_binary64_1460` `rem-exp-log_binary64_1482` `*-commutative_binary64_1373` `exp-sum_binary64_1488`
1×	`sum-log_binary64_1533` `div-inv_binary64_1439` `distribute-lft-out_binary64_1393` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522`

Counts

4 → 118

Calls

8 calls:

34.0ms	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
21.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(exp.f64 (+.f64 z -15/2))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))

series208.0ms (0%)

Counts

4 → 9

Calls

4 calls:

97.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
94.0ms	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
17.0ms	(exp.f64 (+.f64 z -15/2))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 583 to 508 computations (12.9% saved)

simplify80.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5296	4300

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))
0.0b	(pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))
0.0b	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))
0.0b	(sin.f64 (.f64 (.f64 PI.f64 (sqrt.f64 z)) (sqrt.f64 z)))
0.1b	(*.f64 PI.f64 (sqrt.f64 z))
0.2b	(.f64 (.f64 PI.f64 (sqrt.f64 z)) (sqrt.f64 z))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_1480`
16×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `pow1_binary64_1503`
14×	`add-sqr-sqrt_binary64_1464`
11×	`prod-exp_binary64_1491`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`sqrt-prod_binary64_1458`
7×	`cbrt-unprod_binary64_1475`
6×	`pow-prod-down_binary64_1513`
5×	`associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481`
3×	`*-commutative_binary64_1373`
2×	`sqrt-pow1_binary64_1460` `unswap-sqr_binary64_1410`
1×	`associate-r/_binary64_1384` `pow-exp_binary64_1510` `pow-sub_binary64_1518` `pow1/2_binary64_1522` `associate-l/_binary64_1385` `exp-sum_binary64_1488` `pow-to-exp_binary64_1511`

Counts

4 → 75

Calls

8 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
7.0ms	(.f64 (.f64 PI.f64 (sqrt.f64 z)) (sqrt.f64 z))
5.0ms	(*.f64 PI.f64 (sqrt.f64 z))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(sin.f64 (.f64 (.f64 PI.f64 (sqrt.f64 z)) (sqrt.f64 z)))

series135.0ms (0%)

Counts

4 → 9

Calls

4 calls:

91.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
22.0ms	(.f64 (.f64 PI.f64 (sqrt.f64 z)) (sqrt.f64 z))
21.0ms	(*.f64 PI.f64 (sqrt.f64 z))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 691 to 559 computations (19.1% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4985	1175
1	4985	1175

localize129.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
1.0b	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
1.0b	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite237.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`associate-*r/_binary64_1384` `frac-times_binary64_1452`
69×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
64×	`frac-add_binary64_1450`
61×	`flip3--_binary64_1446` `flip--_binary64_1417`
60×	`associate-*l/_binary64_1385`
18×	`pow1_binary64_1503`
15×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
13×	`add-sqr-sqrt_binary64_1464`
11×	`*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
8×	`pow-prod-down_binary64_1513`
7×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
2×	`sqrt-pow1_binary64_1460` `associate-+l+_binary64_1375` `sub-neg_binary64_1435` `*-commutative_binary64_1373` `associate-+r+_binary64_1374`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 173

Calls

8 calls:

42.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
34.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
18.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series341.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

121.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
113.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
107.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6317 to 5163 computations (18.3% saved)

simplify244.0ms (0%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4903	17581
1	4903	17581

localize126.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
1.0b	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite418.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`frac-times_binary64_1452`
358×	`associate-*l/_binary64_1385`
336×	`flip3--_binary64_1446` `flip--_binary64_1417`
192×	`associate-*r/_binary64_1384`
111×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
48×	`pow1_binary64_1503`
45×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
32×	`pow-prod-down_binary64_1513` `frac-add_binary64_1450`
31×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
8×	`add-log-exp_binary64_1481`
4×	`associate-+l+_binary64_1375` `add-sqr-sqrt_binary64_1464` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-+r+_binary64_1374` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
2×	`sqrt-pow1_binary64_1460` `sum-log_binary64_1533` `+-commutative_binary64_1372`
1×	`associate-r_binary64_1382` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522`

Counts

4 → 355

Calls

8 calls:

40.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
35.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
31.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series364.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

124.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
120.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
120.0ms	(.f64 (.f64 (-.f64 2 z) (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))) (.f64 (.f64 (-.f64 3 z) (-.f64 4 z)) (.f64 (-.f64 5 z) -4992549864024149/36028797018963968)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6759 to 5591 computations (17.3% saved)

simplify421.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4947	35895
1	4947	35895

prune2.8min (28.5%)

Pruning

657 alts after pruning (647 fresh and 10 done)

	Pruned	Kept	Total
New	561	330	891
Fresh	4	317	321
Picked	0	0	0
Done	1	10	11
Total	566	657	1223

Error

0.1b

Counts

1223 → 657

Compiler

Compiled 377804 to 309426 computations (18.1% saved)

localize177.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite167.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
12×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393`
8×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450`
4×	`add-cbrt-cube_binary64_1478` `+-commutative_binary64_1372` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `associate-+r+_binary64_1374` `add-cube-cbrt_binary64_1477`

Counts

4 → 68

Calls

8 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series988.0ms (0.2%)

Counts

4 → 47

Calls

4 calls:

248.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
247.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
246.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
246.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 22728 to 19104 computations (15.9% saved)

simplify86.0ms (0%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5026	2557

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
0.0b	(/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))
0.0b	(pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))
0.0b	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))
0.1b	(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z)
0.5b	(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite79.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64_1480`
32×	`add-cbrt-cube_binary64_1478`
27×	`prod-exp_binary64_1491`
13×	`cbrt-unprod_binary64_1475`
12×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503`
10×	`add-cube-cbrt_binary64_1477` `div-exp_binary64_1493`
8×	`associate-r_binary64_1382` `associate-l_binary64_1383`
6×	`cbrt-undiv_binary64_1476` `times-frac_binary64_1448`
4×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
3×	`associate-/r_binary64_1386` `pow-exp_binary64_1510` `pow-prod-down_binary64_1513` `associate-l/_binary64_1385` `pow-to-exp_binary64_1511`
2×	`sqrt-pow1_binary64_1460` `div-inv_binary64_1439` `*-commutative_binary64_1373` `pow-sub_binary64_1518` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `sqrt-prod_binary64_1458` `distribute-rgt-in_binary64_1392` `pow1/2_binary64_1522` `exp-sum_binary64_1488` `unswap-sqr_binary64_1410`

Counts

4 → 96

Calls

8 calls:

32.0ms	(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
18.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z)
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))

series315.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

129.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z)
101.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
85.0ms	(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) z) (+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 583 to 509 computations (12.7% saved)

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5029	3415

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
0.0b	(/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))
0.0b	(pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))
0.0b	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))
0.7b	(cbrt.f64 z)
0.7b	(cbrt.f64 z)
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_1480`
9×	`add-cbrt-cube_binary64_1478` `pow1_binary64_1503`
7×	`add-sqr-sqrt_binary64_1464` `prod-exp_binary64_1491` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`cbrt-prod_binary64_1473`
4×	`associate-r_binary64_1382` `add-log-exp_binary64_1481`
3×	`cbrt-unprod_binary64_1475`
2×	`sqrt-pow1_binary64_1460` `pow-prod-down_binary64_1513` `pow1/3_binary64_1524`
1×	`associate-r/_binary64_1384` `pow-exp_binary64_1510` `associate-l_binary64_1383` `-commutative_binary64_1373` `pow-sub_binary64_1518` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `associate-*l/_binary64_1385` `exp-sum_binary64_1488` `pow-to-exp_binary64_1511`

Counts

4 → 54

Calls

8 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
0.0ms	(+.f64 777369958913643152449373/2951479051793528258560 (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))

series264.0ms (0%)

Counts

4 → 9

Calls

4 calls:

100.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
84.0ms	(cbrt.f64 z)
79.0ms	(cbrt.f64 z)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 727 to 595 computations (18.2% saved)

simplify75.0ms (0%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4948	903
1	4948	903

localize136.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
1.0b	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b	(/.f64 (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 (-.f64 27 (pow.f64 z 3)) -6214088902520669/35184372088832))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.f64 3 z)))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite270.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`frac-times_binary64_1452`
98×	`associate-*r/_binary64_1384`
75×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
64×	`frac-add_binary64_1450`
62×	`associate-*l/_binary64_1385`
61×	`flip3--_binary64_1446` `flip--_binary64_1417`
38×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
26×	`associate-/l/_binary64_1389`
17×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
9×	`pow1_binary64_1503`
8×	`cbrt-undiv_binary64_1476` `associate-/r/_binary64_1388` `add-cube-cbrt_binary64_1477` `div-exp_binary64_1493`
6×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
5×	`associate-r_binary64_1382`
3×	`associate-l_binary64_1383`
2×	`sqrt-pow1_binary64_1460` `associate-+l+_binary64_1375` `sub-neg_binary64_1435` `pow-prod-down_binary64_1513` `associate-+r+_binary64_1374`
1×	`associate-/r_binary64_1386` `sum-log_binary64_1533` `times-frac_binary64_1448` `div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l_binary64_1387` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `frac-2neg_binary64_1453` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 189

Calls

8 calls:

41.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
34.0ms	(/.f64 (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 (-.f64 27 (pow.f64 z 3)) -6214088902520669/35184372088832))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.f64 3 z)))))
30.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))

series361.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

123.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
119.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
119.0ms	(/.f64 (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 (-.f64 27 (pow.f64 z 3)) -6214088902520669/35184372088832))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.f64 3 z)))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6637 to 5371 computations (19.1% saved)

simplify277.0ms (0%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4965	18968
1	4965	18968

localize151.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(/.f64 5950736089418501/8796093022208 (-.f64 1 z))
0.0b	(+.f64 31828687130190046991845674001698638924308767282431494685437358695710790509958860147515625/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584 (pow.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) 3))
0.0b	(+.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) -316912650056936879084143652025/316912650057057350374175801344)
1.0b	(.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) -316912650056936879084143652025/316912650057057350374175801344)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite211.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`associate-*r/_binary64_1384`
42×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
32×	`frac-times_binary64_1452` `frac-add_binary64_1450`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `associate-*l/_binary64_1385`
12×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
8×	`add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
7×	`*-un-lft-identity_binary64_1442`
5×	`cbrt-unprod_binary64_1475` `add-sqr-sqrt_binary64_1464` `prod-exp_binary64_1491` `add-cube-cbrt_binary64_1477`
4×	`associate-+l+_binary64_1375` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `associate-+r+_binary64_1374`
2×	`sqrt-pow1_binary64_1460` `sum-log_binary64_1533` `+-commutative_binary64_1372`
1×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `sqrt-prod_binary64_1458` `pow1/2_binary64_1522` `div-exp_binary64_1493`

Counts

4 → 115

Calls

8 calls:

50.0ms	(.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) -316912650056936879084143652025/316912650057057350374175801344)))
32.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
30.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
0.0ms	(+.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) -316912650056936879084143652025/316912650057057350374175801344)

series470.0ms (0.1%)

Counts

4 → 22

Calls

4 calls:

202.0ms	(.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312) (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)) -316912650056936879084143652025/316912650057057350374175801344)))
136.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
132.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9116 to 7558 computations (17.1% saved)

simplify191.0ms (0%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4908	9508
1	4908	9508

prune1.8min (18.3%)

Pruning

921 alts after pruning (910 fresh and 11 done)

	Pruned	Kept	Total
New	347	280	627
Fresh	12	630	642
Picked	0	0	0
Done	4	11	15
Total	363	921	1284

Error

0.1b

Counts

1284 → 921

Compiler

Compiled 149948 to 121564 computations (18.9% saved)

simplify18.2s (3.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	18460	831244

regimes1.4min (14.6%)

Compiler: Compiled 1097000 to 909392 computations (17.1% saved)

bsearch0.0ms (0%)

regimes18.4s (3.1%)

Compiler: Compiled 248904 to 206536 computations (17% saved)

bsearch0.0ms (0%)

regimes5.6s (1%)

Compiler: Compiled 80950 to 68666 computations (15.2% saved)

bsearch0.0ms (0%)

regimes1.8s (0.3%)

Compiler: Compiled 25600 to 22256 computations (13.1% saved)

bsearch0.0ms (0%)

regimes219.0ms (0%)

Compiler: Compiled 2447 to 2088 computations (14.7% saved)

bsearch0.0ms (0%)

regimes206.0ms (0%)

Compiler: Compiled 2285 to 1956 computations (14.4% saved)

bsearch0.0ms (0%)

regimes137.0ms (0%)

Compiler: Compiled 1451 to 1260 computations (13.2% saved)

bsearch0.0ms (0%)

regimes16.0ms (0%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch159.0ms (0%)

Steps

Iters	Range		Point
9	-1.5910327964005676e-307	7.093569254559865e-302	5.471443429802367e-309

Compiler

Compiled 1 to 1 computations (0% saved)

regimes13.0ms (0%)

Compiler: Compiled 4 to 6 computations (-50% saved)

bsearch35.0ms (0%)

Compiler: Compiled 826 to 688 computations (16.7% saved)

simplify19.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	336	1261
1	336	1261

end0.0ms (0%)

sample57.4s (9.7%)

Algorithm

1×

intervals

Results

42.6s	3815×	body	8192	exit
2.5s	8000×	body	128	valid
241.0ms	11898×	pre	128	true
28.0ms	83×	body	128	invalid

Compiler

Compiled 549968 to 455906 computations (17.1% saved)