Details

analyze100.0ms (1.3%)

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)

sample82.0ms (1%)

Algorithm

1×

intervals

Results

34.0ms	121×	body	1024	valid
21.0ms	38×	body	2048	valid
7.0ms	38×	body	128	valid
6.0ms	32×	body	512	valid
3.0ms	27×	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

37.5b

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))
5.3b	(sin.f64 (+.f64 x eps))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

19.3b

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`sin-sum_binary64_1916` `pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
1×	`diff-sin_binary64_1933` `diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720`

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)

series136.0ms (1.7%)

Error

16.2b

Counts

2 → 23

Calls

2 calls:

71.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
41.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 649 to 390 computations (39.9% saved)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

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

0.3b

Counts

50 → 3

Compiler

Compiled 628 to 205 computations (67.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
0.2b	(*.f64 (sin.f64 eps) (cos.f64 x))
0.2b	(*.f64 (cos.f64 eps) (sin.f64 x))
2.4b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite88.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1805`
11×	`add-log-exp_binary64_1822` `*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818`
8×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`associate-l_binary64_1724` `associate-r_binary64_1723`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`sum-log_binary64_1874` `diff-log_binary64_1875` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
1×	`flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720` `sin-cos-mult_binary64_1939` `flip3-+_binary64_1786` `flip-+_binary64_1757` `+-commutative_binary64_1713`

Counts

4 → 66

Calls

4 calls:

8.0ms	(-.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)

series550.0ms (7%)

Error

0.3b

Counts

4 → 40

Calls

4 calls:

186.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
152.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
97.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))
92.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1604 to 877 computations (45.3% saved)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5150	1793

prune99.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Error

0.1b

Counts

109 → 11

Compiler

Compiled 2177 to 628 computations (71.2% 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))))
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)

rewrite115.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

11×	`*-un-lft-identity_binary64_1783`
10×	`add-log-exp_binary64_1822`
8×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818`
4×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757`
3×	`sum-log_binary64_1874` `difference-of-sqr--1_binary64_1754` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713` `cbrt-prod_binary64_1814`
2×	`cbrt-div_binary64_1815`
1×	`pow1/3_binary64_1865`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 eps) -1)
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)

Compiler

Compiled 2746 to 1153 computations (58% saved)

series699.0ms (8.9%)

Error

0.1b

Counts

4 → 22

Calls

4 calls:

582.0ms	(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)
24.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 3319 to 1810 computations (45.5% saved)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4964	1359
1	4964	1359

prune155.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	71	14	85

Error

0.1b

Counts

85 → 14

Compiler

Compiled 4177 to 1827 computations (56.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.5b	(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
1.5b	(-.f64 (cos.f64 eps) 1)
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)

rewrite162.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
10×	`add-log-exp_binary64_1822`
8×	`add-cube-cbrt_binary64_1818` `log-pow_binary64_1872`
7×	`exp-prod_binary64_1835` `log-prod_binary64_1869`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`pow1_binary64_1844`
4×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `exp-sum_binary64_1829`
2×	`sum-log_binary64_1874` `flip3-+_binary64_1786` `flip-+_binary64_1757` `difference-of-sqr--1_binary64_1754` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713` `sub-neg_binary64_1776` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `flip--_binary64_1758` `exp-diff_binary64_1831` `log-div_binary64_1870` `rem-log-exp_binary64_1824`

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)

series180.0ms (2.3%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

87.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))
24.0ms	(+.f64 (cos.f64 eps) -1)
23.0ms	(+.f64 (cos.f64 eps) -1)
21.0ms	(-.f64 (cos.f64 eps) 1)

Compiler

Compiled 2018 to 1085 computations (46.2% saved)

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4888	767
1	4888	767

prune145.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Error

0.1b

Counts

97 → 14

Compiler

Compiled 4092 to 1756 computations (57.1% saved)

regimes593.0ms (7.5%)

Accuracy

Total 0.3b remaining (72.4%)

Threshold costs 0.3b (72.4%)

Compiler

Compiled 7826 to 4450 computations (43.1% 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%)

sample4.3s (54.9%)

Algorithm

1×

intervals

Results

1.0s	3472×	body	1024	valid
633.0ms	1240×	body	2048	valid
285.0ms	1403×	body	512	valid
79.0ms	1297×	body	128	valid
78.0ms	588×	body	256	valid

Compiler

Compiled 2618 to 1497 computations (42.8% saved)

Details

analyze100.0ms (1.3%)

sample82.0ms (1%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite35.0ms (0.4%)

series136.0ms (1.7%)

simplify60.0ms (0.8%)

prune48.0ms (0.6%)

localize11.0ms (0.1%)

rewrite88.0ms (1.1%)

series550.0ms (7%)

simplify76.0ms (1%)

prune99.0ms (1.3%)

localize17.0ms (0.2%)

rewrite115.0ms (1.5%)

series699.0ms (8.9%)

simplify80.0ms (1%)

prune155.0ms (2%)

localize24.0ms (0.3%)

rewrite162.0ms (2.1%)

series180.0ms (2.3%)

simplify82.0ms (1%)

prune145.0ms (1.8%)

regimes593.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.3s (54.9%)

Profiling