Details

analyze1.9s (3.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115
0	1	1
1	1	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)

sample1.5s (2.5%)

Algorithm

1×

intervals

Results

1.4s	123×	body	8192	exit
75.0ms	256×	body	128	valid
6.0ms	381×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune16.0ms (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

1.7b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite950.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

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×	`pow1_binary64_1503` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
7×	`prod-exp_binary64_1491`
5×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
4×	`associate-r_binary64_1382`
3×	`cbrt-unprod_binary64_1475`
2×	`associate-+l+_binary64_1375` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `sqrt-pow1_binary64_1460`
1×	`pow1/2_binary64_1522` `sqrt-prod_binary64_1458` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `pow-sub_binary64_1518` `associate-r/_binary64_1384` `associate-l/_binary64_1385` `associate-l_binary64_1383` `exp-sum_binary64_1488` `*-commutative_binary64_1373`

Counts

4 → 86

Calls

4 calls:

94.0ms	(+.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)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 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))

Compiler

Compiled 10066 to 7936 computations (21.2% saved)

series392.0ms (0.7%)

Error

0.3b

Counts

4 → 22

Calls

4 calls:

188.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
89.0ms	(+.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)))
37.0ms	(+.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 3444 to 2750 computations (20.2% saved)

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5189	8306

prune743.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Error

0.2b

Counts

110 → 6

Compiler

Compiled 11699 to 9150 computations (21.8% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite226.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 78

Calls

4 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)))
8.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3848 to 2484 computations (35.4% saved)

series291.0ms (0.5%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

184.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
42.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
34.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1811 to 1419 computations (21.6% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4951	1669
1	4951	1669

prune242.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Error

0.0b

Counts

96 → 12

Compiler

Compiled 4916 to 3283 computations (33.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
1.0b	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite250.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`add-sqr-sqrt_binary64_1464`
19×	`*-un-lft-identity_binary64_1442`
17×	`add-cube-cbrt_binary64_1477`
16×	`associate-r_binary64_1382`
13×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
12×	`pow1_binary64_1503`
9×	`times-frac_binary64_1448`
6×	`prod-exp_binary64_1491` `unpow-prod-down_binary64_1521`
5×	`associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481` `pow-prod-down_binary64_1513` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `unpow-prod-up_binary64_1520`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`sqrt-pow1_binary64_1460` `sqr-pow_binary64_1414` `*-commutative_binary64_1373`
1×	`pow1/2_binary64_1522` `sqrt-prod_binary64_1458` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `pow-sub_binary64_1518` `associate-*r/_binary64_1384` `exp-sum_binary64_1488` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `sub-neg_binary64_1435` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 90

Calls

4 calls:

17.0ms	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
3.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4452 to 2885 computations (35.2% saved)

series204.0ms (0.4%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

102.0ms	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
43.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
33.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1660 to 1318 computations (20.6% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4938	1651
1	4938	1651

prune260.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Error

0.0b

Counts

114 → 12

Compiler

Compiled 5479 to 3656 computations (33.3% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
1.0b	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite229.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-sqr-sqrt_binary64_1464`
19×	`associate-r_binary64_1382`
14×	`pow1_binary64_1503`
13×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `*-un-lft-identity_binary64_1442`
11×	`add-cube-cbrt_binary64_1477`
8×	`associate-l_binary64_1383`
7×	`prod-exp_binary64_1491`
6×	`unpow-prod-down_binary64_1521`
5×	`pow-prod-down_binary64_1513` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481` `unpow-prod-up_binary64_1520`
3×	`cancel-sign-sub-inv_binary64_1408` `*-commutative_binary64_1373`
2×	`sqrt-pow1_binary64_1460` `sqr-pow_binary64_1414`
1×	`pow1/2_binary64_1522` `sqrt-prod_binary64_1458` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `pow-sub_binary64_1518` `associate-*r/_binary64_1384` `exp-sum_binary64_1488` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `sub-neg_binary64_1435`

Counts

4 → 81

Calls

4 calls:

15.0ms	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3700 to 2778 computations (24.9% saved)

series143.0ms (0.2%)

Error

0.0b

Counts

4 → 10

Calls

4 calls:

66.0ms	(*.f64 (exp.f64 (+.f64 -15/2 z)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))
32.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
24.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1209 to 997 computations (17.5% saved)

simplify88.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4894	1138
1	4894	1138

prune213.0ms (0.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	92	11	103

Error

0.0b

Counts

103 → 11

Compiler

Compiled 3949 to 2979 computations (24.6% saved)

regimes787.0ms (1.4%)

Accuracy

Total 0.4b remaining (92.4%)

Threshold costs 0.4b (92.4%)

Compiler

Compiled 11792 to 9510 computations (19.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	113	133
1	113	133

end0.0ms (0%)

sample49.1s (84.8%)

Algorithm

1×

intervals

Results

41.7s	3792×	body	8192	exit
2.4s	8000×	body	128	valid
205.0ms	11874×	pre	128	true
27.0ms	82×	body	128	invalid

Compiler

Compiled 5981 to 4827 computations (19.3% saved)

Details

analyze1.9s (3.2%)

sample1.5s (2.5%)

simplify50.0ms (0.1%)

prune16.0ms (0%)

localize53.0ms (0.1%)

rewrite950.0ms (1.6%)

series392.0ms (0.7%)

simplify95.0ms (0.2%)

prune743.0ms (1.3%)

localize29.0ms (0%)

rewrite226.0ms (0.4%)

series291.0ms (0.5%)

simplify78.0ms (0.1%)

prune242.0ms (0.4%)

localize29.0ms (0.1%)

rewrite250.0ms (0.4%)

series204.0ms (0.4%)

simplify79.0ms (0.1%)

prune260.0ms (0.4%)

localize29.0ms (0.1%)

rewrite229.0ms (0.4%)

series143.0ms (0.2%)

simplify88.0ms (0.2%)

prune213.0ms (0.4%)

regimes787.0ms (1.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample49.1s (84.8%)

Profiling