Details

analyze987.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample57.0ms (0%)

Algorithm

1×

intervals

Results

23.0ms	107×	body	1024	valid
14.0ms	35×	body	2048	valid
7.0ms	48×	body	512	valid
2.0ms	24×	body	256	valid
2.0ms	42×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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

37.8b

Counts

2 → 1

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

5.5b	(tan.f64 (+.f64 x eps))
1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.5b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `tan-quot_binary64_1601`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `frac-sub_binary64_1451` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-sum_binary64_1577`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

2 → 27

Calls

4 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
0.0ms	(tan.f64 (+.f64 x eps))

series447.0ms (0.3%)

Counts

2 → 23

Calls

2 calls:

285.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
163.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 904 to 607 computations (32.9% saved)

simplify43.0ms (0%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5755	1398

prune220.0ms (0.2%)

Pruning

37 alts after pruning (36 fresh and 1 done)

	Pruned	Kept	Total
New	14	36	50
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	14	37	51

Error

0.2b

Counts

51 → 37

Compiler

Compiled 1738 to 894 computations (48.6% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
16×	`add-cube-cbrt_binary64_1477`
13×	`times-frac_binary64_1448`
9×	`tan-quot_binary64_1601`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-/l/_binary64_1389` `associate-l*_binary64_1383`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `frac-times_binary64_1452` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 88

Calls

8 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.4%)

Counts

4 → 47

Calls

4 calls:

988.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
548.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
266.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
212.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2088 to 1335 computations (36.1% saved)

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4958	4043
1	4958	4043

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`times-frac_binary64_1448` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
3×	`associate-/r_binary64_1386` `add-cbrt-cube_binary64_1478` `associate-/l_binary64_1387` `add-exp-log_binary64_1480`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `quot-tan_binary64_1602` `pow1_binary64_1503` `div-exp_binary64_1493`

Counts

1 → 28

Calls

2 calls:

4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))

series36.0ms (0%)

Counts

1 → 5

Calls

1 calls:

36.0ms

(/.f64 (sin.f64 eps) (cos.f64 eps))

Compiler

Compiled 60 to 58 computations (3.3% saved)

simplify123.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4490	445
1	4490	445

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

5.5b	(tan.f64 (+.f64 x eps))
4.8b	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
0.6b	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
0.2b	(log.f64 (tan.f64 (+.f64 x eps)))
0.2b	(log.f64 (tan.f64 (+.f64 x eps)))
0.6b	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
4.8b	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
5.5b	(tan.f64 (+.f64 x eps))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
8×	`add-cube-cbrt_binary64_1477`
7×	`log-prod_binary64_1528`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `log-div_binary64_1529` `tan-quot_binary64_1601`
5×	`add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `exp-prod_binary64_1494` `exp-diff_binary64_1490` `exp-sum_binary64_1488` `tan-sum_binary64_1577`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`log-pow_binary64_1531` `frac-sub_binary64_1451` `difference-of-squares_binary64_1411`
1×	`sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

4 → 59

Calls

8 calls:

10.0ms	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
7.0ms	(tan.f64 (+.f64 x eps))
5.0ms	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
4.0ms	(log.f64 (tan.f64 (+.f64 x eps)))
0.0ms	(log.f64 (tan.f64 (+.f64 x eps)))

series1.3s (0.9%)

Counts

4 → 38

Calls

4 calls:

446.0ms	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
353.0ms	(log.f64 (tan.f64 (+.f64 x eps)))
336.0ms	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
144.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1933 to 1110 computations (42.6% saved)

simplify54.0ms (0%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5311	1959

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (cos.f64 eps) 2)
0.2b	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0b	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)))
0.2b	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
0.3b	(pow.f64 (cos.f64 eps) 2)
0.3b	(pow.f64 (sin.f64 eps) 2)
3.7b	(*.f64 x (pow.f64 (sin.f64 eps) 2))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64_1480`
21×	`add-sqr-sqrt_binary64_1464`
16×	`unpow-prod-down_binary64_1521`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
12×	`prod-exp_binary64_1491` `div-exp_binary64_1493`
11×	`add-cbrt-cube_binary64_1478`
10×	`pow-exp_binary64_1510` `pow-to-exp_binary64_1511`
8×	`associate-r_binary64_1382` `associate-/r*_binary64_1386` `times-frac_binary64_1448`
6×	`unpow2_binary64_1507` `pow-unpow_binary64_1519` `sqr-pow_binary64_1414` `pow1_binary64_1503`
4×	`add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`associate-l_binary64_1383`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `pow-pow_binary64_1514`
1×	`div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l_binary64_1387` `-commutative_binary64_1373` `frac-2neg_binary64_1453`

Counts

4 → 104

Calls

8 calls:

8.0ms	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
6.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
3.0ms	(pow.f64 (sin.f64 eps) 2)
2.0ms	(pow.f64 (cos.f64 eps) 2)
0.0ms	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)))

series358.0ms (0.3%)

Counts

4 → 23

Calls

4 calls:

210.0ms	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
95.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
27.0ms	(pow.f64 (sin.f64 eps) 2)
26.0ms	(pow.f64 (cos.f64 eps) 2)

Compiler

Compiled 730 to 533 computations (27% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5047	1585

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
0.3b	(cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
0.3b	(*.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
0.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.5b	(tan.f64 (+.f64 x eps))
5.5b	(tan.f64 (+.f64 x eps))
5.5b	(tan.f64 (+.f64 x eps))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
6×	`add-log-exp_binary64_1481` `tan-quot_binary64_1601`
5×	`add-cube-cbrt_binary64_1477`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-sum_binary64_1577`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`frac-sub_binary64_1451`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

4 → 45

Calls

8 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))

series775.0ms (0.6%)

Counts

4 → 43

Calls

4 calls:

282.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
166.0ms	(tan.f64 (+.f64 x eps))
165.0ms	(tan.f64 (+.f64 x eps))
162.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 2944 to 1587 computations (46.1% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4976	2070
1	4976	2070

prune6.8s (4.8%)

Pruning

271 alts after pruning (265 fresh and 6 done)

	Pruned	Kept	Total
New	243	237	480
Fresh	3	28	31
Picked	0	0	0
Done	0	6	6
Total	246	271	517

Error

0.1b

Counts

517 → 271

Compiler

Compiled 15835 to 6941 computations (56.2% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
27×	`times-frac_binary64_1448`
24×	`add-cube-cbrt_binary64_1477`
17×	`unpow-prod-down_binary64_1521`
11×	`add-exp-log_binary64_1480`
8×	`add-cbrt-cube_binary64_1478` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481`
7×	`tan-quot_binary64_1601`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414`
4×	`difference-of-squares_binary64_1411`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-l*_binary64_1383` `div-exp_binary64_1493`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `pow-exp_binary64_1510` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `frac-add_binary64_1450` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 105

Calls

8 calls:

19.0ms	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
10.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.4%)

Counts

4 → 47

Calls

4 calls:

988.0ms	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
528.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
245.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
190.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2152 to 1399 computations (35% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4985	4772
1	4985	4772

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
0.2b	(*.f64 (tan.f64 x) (sin.f64 eps))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))

rewrite59.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1442`
43×	`add-sqr-sqrt_binary64_1464`
28×	`times-frac_binary64_1448`
21×	`add-cube-cbrt_binary64_1477`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
12×	`difference-of-squares_binary64_1411`
9×	`associate-/r*_binary64_1386`
7×	`distribute-lft-out_binary64_1393`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
5×	`associate-/l*_binary64_1387` `tan-quot_binary64_1601`
4×	`associate-/l/_binary64_1389`
3×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `div-exp_binary64_1493`
2×	`cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `associate-/r/_binary64_1388` `clear-num_binary64_1441` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-2neg_binary64_1453` `prod-exp_binary64_1491` `associate-*l/_binary64_1385`
1×	`sub-neg_binary64_1435` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `unswap-sqr_binary64_1410`

Counts

4 → 110

Calls

8 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
12.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 eps))
0.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))

series2.0s (1.4%)

Counts

4 → 47

Calls

4 calls:

985.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
542.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
256.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
185.0ms	(*.f64 (tan.f64 x) (sin.f64 eps))

Compiler

Compiled 2194 to 1393 computations (36.5% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4978	5297
1	4978	5297

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.6b	(-.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite182.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

395×	`times-frac_binary64_1448`
309×	`*-un-lft-identity_binary64_1442`
233×	`sqrt-prod_binary64_1458`
219×	`add-sqr-sqrt_binary64_1464`
193×	`add-cube-cbrt_binary64_1477`
57×	`distribute-lft-out_binary64_1393`
35×	`associate-/r*_binary64_1386`
30×	`sqrt-div_binary64_1459`
28×	`associate-/r/_binary64_1388`
25×	`tan-quot_binary64_1601`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`div-inv_binary64_1439` `associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450`
7×	`difference-of-squares_binary64_1411`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
5×	`associate-/l/_binary64_1389`
4×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
3×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383`
2×	`clear-num_binary64_1441` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-2neg_binary64_1453`
1×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `sub-neg_binary64_1435` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `diff-log_binary64_1534` `frac-times_binary64_1452` `prod-exp_binary64_1491` `div-sub_binary64_1447` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 342

Calls

8 calls:

80.0ms	(-.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
21.0ms	(/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))))
11.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))

series2.4s (1.7%)

Counts

4 → 44

Calls

4 calls:

974.0ms	(-.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
635.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
544.0ms	(/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))))
225.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2592 to 1575 computations (39.2% saved)

simplify244.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

386 → 386

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4970	19248
1	4970	19248

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite83.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_1464`
13×	`tan-quot_binary64_1601` `*-un-lft-identity_binary64_1442`
11×	`add-cube-cbrt_binary64_1477`
10×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
9×	`associate-r_binary64_1382` `associate-l_binary64_1383`
6×	`times-frac_binary64_1448` `add-log-exp_binary64_1481`
5×	`difference-of-squares_binary64_1411`
3×	`associate-r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-times_binary64_1452` `prod-exp_binary64_1491` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`
2×	`cbrt-prod_binary64_1473`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

4 → 84

Calls

8 calls:

54.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series1.8s (1.3%)

Counts

4 → 47

Calls

4 calls:

1.0s	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
272.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
258.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
257.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3036 to 1841 computations (39.4% saved)

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5049	3583

prune20.8s (14.9%)

Pruning

533 alts after pruning (524 fresh and 9 done)

	Pruned	Kept	Total
New	536	290	826
Fresh	26	234	260
Picked	0	0	0
Done	2	9	11
Total	564	533	1097

Error

0.0b

Counts

1097 → 533

Compiler

Compiled 34937 to 15167 computations (56.6% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
16×	`add-cube-cbrt_binary64_1477`
13×	`times-frac_binary64_1448`
9×	`tan-quot_binary64_1601`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-/l/_binary64_1389` `associate-l*_binary64_1383`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `frac-times_binary64_1452` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 88

Calls

8 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.4%)

Counts

4 → 47

Calls

4 calls:

965.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
527.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
264.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
198.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2216 to 1463 computations (34% saved)

simplify108.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4958	4043
1	4958	4043

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/3 (pow.f64 eps 3))
0.0b	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0b	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.1b	(*.f64 1/3 (pow.f64 eps 3))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
12×	`associate-r_binary64_1382`
7×	`add-exp-log_binary64_1480`
6×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-cbrt-cube_binary64_1478` `cube-prod_binary64_1470` `add-log-exp_binary64_1481` `unpow-prod-down_binary64_1521` `unswap-sqr_binary64_1410`
3×	`associate-l_binary64_1383` `prod-exp_binary64_1491`
2×	`sqr-pow_binary64_1414` `pow1_binary64_1503`
1×	`cube-mult_binary64_1472` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `pow-exp_binary64_1510` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `unpow3_binary64_1508` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`

Counts

2 → 42

Calls

4 calls:

7.0ms	(*.f64 1/3 (pow.f64 eps 3))
3.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0ms	(*.f64 1/3 (pow.f64 eps 3))

series96.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

64.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
32.0ms	(*.f64 1/3 (pow.f64 eps 3))

Compiler

Compiled 95 to 98 computations (-3.2% saved)

simplify48.0ms (0%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5017	527

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.6b	(exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
5.3b	(-.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1464`
16×	`*-un-lft-identity_binary64_1442`
10×	`add-cube-cbrt_binary64_1477`
9×	`log-prod_binary64_1528` `tan-quot_binary64_1601`
8×	`pow1_binary64_1503`
7×	`add-exp-log_binary64_1480`
6×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `log-div_binary64_1529`
5×	`difference-of-squares_binary64_1411` `exp-sum_binary64_1488`
4×	`times-frac_binary64_1448` `exp-prod_binary64_1494`
3×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `exp-diff_binary64_1490`
2×	`log-pow_binary64_1531` `distribute-lft-out_binary64_1393` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `unpow-prod-down_binary64_1521`
1×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `diff-log_binary64_1534` `frac-times_binary64_1452` `sqr-pow_binary64_1414` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 77

Calls

8 calls:

22.0ms	(-.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
6.0ms	(exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series1.9s (1.4%)

Counts

4 → 40

Calls

4 calls:

838.0ms	(-.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
449.0ms	(exp.f64 (log.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
370.0ms	(log.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
237.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2181 to 1361 computations (37.6% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5013	2866

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x)
0.0b	(.f64 2/15 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5)))
0.0b	(+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))))
0.0b	(+.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) (+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5)))))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.8b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))
1.0b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))
1.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (+.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) (+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))))))) (tan.f64 x))

rewrite86.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64_1464`
35×	`times-frac_binary64_1448`
34×	`*-un-lft-identity_binary64_1442`
32×	`add-exp-log_binary64_1480` `add-cube-cbrt_binary64_1477`
26×	`associate-l_binary64_1383`
19×	`associate-r_binary64_1382`
16×	`add-cbrt-cube_binary64_1478`
14×	`unswap-sqr_binary64_1410`
12×	`prod-exp_binary64_1491`
10×	`unpow-prod-down_binary64_1521`
7×	`div-exp_binary64_1493`
6×	`add-log-exp_binary64_1481` `sqr-pow_binary64_1414`
5×	`cube-prod_binary64_1470`
4×	`cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `pow1_binary64_1503` `pow-to-exp_binary64_1511`
3×	`cbrt-undiv_binary64_1476` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `div-inv_binary64_1439` `associate-/l_binary64_1387`
2×	`-commutative_binary64_1373` `difference-of-squares_binary64_1411` `associate-l/_binary64_1385`
1×	`cube-mult_binary64_1472` `sub-neg_binary64_1435` `clear-num_binary64_1441` `flip3--_binary64_1446` `frac-sub_binary64_1451` `flip--_binary64_1417` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `unpow3_binary64_1508` `quot-tan_binary64_1602` `tan-quot_binary64_1601` `distribute-lft-out--_binary64_1394`

Counts

4 → 139

Calls

8 calls:

37.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (+.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) (+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))))))) (tan.f64 x))
14.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))
10.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0ms	(+.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) (+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5)))))

series1.7s (1.2%)

Counts

4 → 26

Calls

4 calls:

1.3s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (+.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) (+.f64 (.f64 1/3 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))) (.f64 2/15 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))))))) (tan.f64 x))
181.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 5))
170.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 x 3))
33.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))

Compiler

Compiled 2876 to 1833 computations (36.3% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5156	5145

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0b	(/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps)))))))
0.0b	(-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))
1.5b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))))))) (tan.f64 x))
6.4b	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))
6.4b	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))

rewrite147.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`pow1_binary64_1503`
41×	`tan-quot_binary64_1601`
32×	`sqrt-pow1_binary64_1460`
30×	`sqrt-div_binary64_1459`
25×	`add-sqr-sqrt_binary64_1464`
22×	`pow-prod-down_binary64_1513`
19×	`frac-times_binary64_1452`
13×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
12×	`pow1/2_binary64_1522`
11×	`*-un-lft-identity_binary64_1442`
10×	`pow-prod-up_binary64_1512`
9×	`add-cube-cbrt_binary64_1477`
6×	`add-cbrt-cube_binary64_1478` `times-frac_binary64_1448` `pow-sqr_binary64_1415` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `sqrt-prod_binary64_1458`
5×	`difference-of-squares_binary64_1411`
4×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`cbrt-prod_binary64_1473`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `sub-neg_binary64_1435` `pow-plus_binary64_1505` `flip3--_binary64_1446` `frac-sub_binary64_1451` `*-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `flip--_binary64_1417` `diff-log_binary64_1534` `prod-exp_binary64_1491` `rem-square-sqrt_binary64_1454` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 113

Calls

8 calls:

76.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))))))) (tan.f64 x))
35.0ms	(.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))
4.0ms	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))
4.0ms	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0ms	(-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))

series1.9s (1.3%)

Counts

4 → 35

Calls

4 calls:

1.1s	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (-.f64 1 (.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))))))) (tan.f64 x))
283.0ms	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))
275.0ms	(.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))
239.0ms	(sqrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))

Compiler

Compiled 2724 to 1617 computations (40.6% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5104	3494

prune32.7s (23.4%)

Pruning

731 alts after pruning (717 fresh and 14 done)

	Pruned	Kept	Total
New	395	221	616
Fresh	23	496	519
Picked	0	0	0
Done	0	14	14
Total	418	731	1149

Error

0.0b

Counts

1149 → 731

Compiler

Compiled 16062 to 6065 computations (62.2% saved)

simplify1.1s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5122	61982

regimes16.5s (11.8%)

Compiler: Compiled 105028 to 58966 computations (43.9% saved)

bsearch145.0ms (0.1%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	3.6655339994443544e-07
9	-0.0007981377221361468	-3.656686348929657e-12	-1.7473206182972273e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.7s (2.7%)

Compiler: Compiled 24207 to 16261 computations (32.8% saved)

bsearch87.0ms (0.1%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	2.4205365137533804e-09
9	-0.0007981377221361468	-3.656686348929657e-12	-3.4524649511233764e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes1.1s (0.8%)

Compiler: Compiled 5538 to 4351 computations (21.4% saved)

bsearch74.0ms (0.1%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	3.0131377431129065e-09
9	-0.0007981377221361468	-3.656686348929657e-12	-3.983762250734975e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes732.0ms (0.5%)

Compiler: Compiled 3202 to 2681 computations (16.3% saved)

bsearch75.0ms (0.1%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	4.3750894905222405e-09
9	-0.0007981377221361468	-3.656686348929657e-12	-2.6483423041732394e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes554.0ms (0.4%)

Compiler: Compiled 2371 to 2105 computations (11.2% saved)

bsearch70.0ms (0%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	0.0028560446610936562
9	-0.0007981377221361468	-3.656686348929657e-12	-2.2598987238706772e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes264.0ms (0.2%)

Compiler: Compiled 1519 to 1421 computations (6.5% saved)

bsearch0.0ms (0%)

regimes38.0ms (0%)

Compiler: Compiled 48 to 58 computations (-20.8% saved)

bsearch60.0ms (0%)

Steps

Iters	Range		Point
10	5.143106913767641e-14	0.09580101676021323	0.09455824190685944
9	-177739.4511812354	-0.0007981377221361468	-2.4967221658712426

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes29.0ms (0%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch52.0ms (0%)

Steps

Iters	Range		Point
8	18313058.022212096	9987823704.995243	64304119.503859706
9	-177739.4511812354	-0.0007981377221361468	-24.817807291206645

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes22.0ms (0%)

Compiler: Compiled 10 to 24 computations (-140% saved)

bsearch33.0ms (0%)

Steps

Iters	Range		Point
8	-5.653814581186559e+78	-1.6886318924849538e+74	-1.6383273519735958e+75

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes16.0ms (0%)

Accuracy

Total 0.2b remaining (72.1%)

Threshold costs 0.2b (72.1%)

Compiler

Compiled 8 to 18 computations (-125% saved)

bsearch16.0ms (0%)

Compiler: Compiled 315 to 202 computations (35.9% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	155	466
1	155	466

end0.0ms (0%)

sample30.5s (21.8%)

Algorithm

1×

intervals

Results

850.0ms	3520×	body	1024	valid
563.0ms	1207×	body	2048	valid
212.0ms	1357×	body	512	valid
69.0ms	1334×	body	128	valid
56.0ms	580×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 35822 to 20213 computations (43.6% saved)

Pareto

0.6564069634871619