Details

analyze103.0ms (1.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample73.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	108×	body	1024	valid
18.0ms	36×	body	2048	valid
8.0ms	43×	body	512	valid
3.0ms	51×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (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

35.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.2b	(sin.f64 (+.f64 x eps))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

20.1b

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`add-cube-cbrt_binary64_1477` `cancel-sign-sub-inv_binary64_1408`
2×	`sin-sum_binary64_1575` `pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
1×	`diff-sin_binary64_1592` `diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series142.0ms (1.6%)

Error

13.9b

Counts

2 → 23

Calls

2 calls:

78.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
39.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 649 to 390 computations (39.9% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5076	717

prune48.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.2b

Counts

50 → 3

Compiler

Compiled 635 to 209 computations (67.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
0.1b	(*.f64 (cos.f64 eps) (sin.f64 x))
0.2b	(*.f64 (sin.f64 eps) (cos.f64 x))
2.2b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite100.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1464`
11×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477`
8×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`sum-log_binary64_1533` `diff-log_binary64_1534` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379` `sin-cos-mult_binary64_1598` `flip3-+_binary64_1445` `flip-+_binary64_1416` `+-commutative_binary64_1372`

Counts

4 → 66

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
5.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
5.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1495 to 285 computations (80.9% saved)

series577.0ms (6.6%)

Error

0.2b

Counts

4 → 45

Calls

4 calls:

183.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
147.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
114.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
101.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1864 to 1020 computations (45.3% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5016	1959

prune108.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Error

0.1b

Counts

114 → 11

Compiler

Compiled 2360 to 723 computations (69.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)

rewrite125.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

11×	`*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
8×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477`
4×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`sum-log_binary64_1533` `difference-of-sqr--1_binary64_1413` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372` `cbrt-prod_binary64_1473`
2×	`cbrt-div_binary64_1474`
1×	`pow1/3_binary64_1524`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 2746 to 1153 computations (58% saved)

series720.0ms (8.2%)

Error

0.1b

Counts

4 → 23

Calls

4 calls:

594.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
27.0ms	(+.f64 (cos.f64 eps) -1)
25.0ms	(+.f64 (cos.f64 eps) -1)
23.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 3552 to 1972 computations (44.5% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5910	1610

prune162.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	72	14	86

Error

0.1b

Counts

86 → 14

Compiler

Compiled 4497 to 1999 computations (55.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (cos.f64 eps) 1)
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(+.f64 (cos.f64 eps) -1)
1.4b	(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))

rewrite161.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
8×	`log-pow_binary64_1531` `add-cube-cbrt_binary64_1477`
7×	`exp-prod_binary64_1494` `log-prod_binary64_1528`
6×	`cancel-sign-sub-inv_binary64_1408`
5×	`pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411` `exp-sum_binary64_1488` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
2×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394` `sub-neg_binary64_1435` `sum-log_binary64_1533` `flip3-+_binary64_1445` `flip-+_binary64_1416` `difference-of-sqr--1_binary64_1413` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372`
1×	`exp-diff_binary64_1490` `log-div_binary64_1529` `rem-log-exp_binary64_1483` `diff-log_binary64_1534` `flip3--_binary64_1446` `flip--_binary64_1417`

Counts

4 → 68

Calls

4 calls:

6.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
5.0ms	(-.f64 (cos.f64 eps) 1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 3552 to 1594 computations (55.1% saved)

series190.0ms (2.2%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

92.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
25.0ms	(+.f64 (cos.f64 eps) -1)
24.0ms	(+.f64 (cos.f64 eps) -1)
21.0ms	(-.f64 (cos.f64 eps) 1)

Compiler

Compiled 2018 to 1085 computations (46.2% saved)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4888	767
1	4888	767

prune151.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	83	14	97

Error

0.1b

Counts

97 → 14

Compiler

Compiled 4092 to 1756 computations (57.1% saved)

regimes900.0ms (10.2%)

Accuracy

Total 0.3b remaining (80.7%)

Threshold costs 0.3b (80.7%)

Compiler

Compiled 9552 to 5471 computations (42.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample4.8s (55%)

Algorithm

1×

intervals

Results

1.1s	3450×	body	1024	valid
672.0ms	1292×	body	2048	valid
288.0ms	1366×	body	512	valid
87.0ms	632×	body	256	valid
80.0ms	1257×	body	128	valid
4.0ms	3×	body	4096	valid

Compiler

Compiled 3197 to 1840 computations (42.4% saved)

Details

analyze103.0ms (1.2%)

sample73.0ms (0.8%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite40.0ms (0.5%)

series142.0ms (1.6%)

simplify59.0ms (0.7%)

prune48.0ms (0.6%)

localize12.0ms (0.1%)

rewrite100.0ms (1.1%)

series577.0ms (6.6%)

simplify81.0ms (0.9%)

prune108.0ms (1.2%)

localize17.0ms (0.2%)

rewrite125.0ms (1.4%)

series720.0ms (8.2%)

simplify64.0ms (0.7%)

prune162.0ms (1.8%)

localize28.0ms (0.3%)

rewrite161.0ms (1.8%)

series190.0ms (2.2%)

simplify79.0ms (0.9%)

prune151.0ms (1.7%)

regimes900.0ms (10.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.8s (55%)

Profiling