Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

sample95.0ms (2.2%)

Algorithm

1×

intervals

Results

49.0ms	103×	body	1280	valid
19.0ms	75×	body	640	valid
11.0ms	12×	body	2560	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	27×	body	80	valid

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.1%)

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

Merged error: 35.4b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.7b	(sin.f64 (+.f64 x eps))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series14.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

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

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5348	268

prune39.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.4b

Counts

30 → 3

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-cos-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series38.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(+.f64 x (+.f64 x eps))

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5222	886

prune111.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Merged error: 0.4b

Counts

75 → 8

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-prod_binary64` `exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series35.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
10.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5064	940

prune110.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	73	8	81

Merged error: 0.4b

Counts

81 → 8

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))
0.4b	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
0.5b	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
6×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
8.0ms	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))

series71.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
24.0ms	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
15.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4975	1219
1	4975	1219

prune108.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	82	8	90

Merged error: 0.4b

Counts

90 → 8

regimes148.0ms (3.4%)

Accuracy

Total 0.1b remaining (20.1%)

Threshold costs 0.1b (20.1%)

bsearch70.0ms (1.6%)

Steps

Iters	Range		Point
9	1.9050947580688215e-15	2.086968805494545e-06	7.686797686493851e-09
9	-5818.371851083311	-0.0028689388283919684	-0.0029089008421326404

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms (0%)

sample3.1s (71.3%)

Algorithm

1×

intervals

Results

1.6s	3344×	body	1280	valid
584.0ms	611×	body	2560	valid
527.0ms	1896×	body	640	valid
133.0ms	728×	body	320	valid
63.0ms	1088×	body	80	valid
42.0ms	333×	body	160	valid

Details

analyze2.0ms (0%)

sample95.0ms (2.2%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite12.0ms (0.3%)

series14.0ms (0.3%)

simplify54.0ms (1.3%)

prune39.0ms (0.9%)

localize13.0ms (0.3%)

rewrite31.0ms (0.7%)

series38.0ms (0.9%)

simplify51.0ms (1.2%)

prune111.0ms (2.6%)

localize16.0ms (0.4%)

rewrite42.0ms (1%)

series35.0ms (0.8%)

simplify52.0ms (1.2%)

prune110.0ms (2.6%)

localize16.0ms (0.4%)

rewrite33.0ms (0.8%)

series71.0ms (1.6%)

simplify60.0ms (1.4%)

prune108.0ms (2.5%)

regimes148.0ms (3.4%)

bsearch70.0ms (1.6%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (71.3%)

Profiling