Details

analyze2.0ms

Algorithm

Search

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

sample102.0ms

Algorithm

intervals

Results

44.0ms	96×	body	1280	valid
21.0ms	61×	body	640	valid
18.0ms	19×	body	2560	valid
5.0ms	24×	body	320	valid
2.0ms	41×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 36.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.4b	(sin.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5251	260

prune40.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

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: 0.5b

Counts

30 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

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

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+.f64 x (+.f64 x eps))
13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4984	535
1	4984	535

prune77.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.5b

Counts

53 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series44.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify64.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4905	410
1	4905	410

prune80.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	44	8	52

Merged error: 0.5b

Counts

52 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
4.4b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
3×	`sin-cos-mult_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 64

Calls

4 calls:

7.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
5.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
5.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
10.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
12.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
13.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
30.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4908	846
1	4908	846

prune68.0ms

Filtered

55 candidates to 76 candidates (-38.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	71	13	84

Merged error: 0.4b

Counts

84 → 13

regimes174.0ms

Accuracy

96.6% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 6.0b

bsearch59.0ms

Steps

Iters	Range		Point
4	3.8511709875897413e-38	6.225336684501125e-38	5.519874034867513e-38
9	-0.001946410249595348	-9.494300489779706e-09	-1.1685964086771769e-08

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	65
1	71	65

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	3318×	body	1280	valid
613.0ms	631×	body	2560	valid
525.0ms	1816×	body	640	valid
164.0ms	785×	body	320	valid
67.0ms	1108×	body	80	valid
44.0ms	342×	body	160	valid

Details

analyze2.0ms

sample102.0ms

simplify7.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series14.0ms

simplify71.0ms

prune40.0ms

localize13.0ms

rewrite22.0ms

series24.0ms

simplify68.0ms

prune77.0ms

localize16.0ms

rewrite26.0ms

series44.0ms

simplify64.0ms

prune80.0ms

localize14.0ms

rewrite29.0ms

series70.0ms

simplify50.0ms

prune68.0ms

regimes174.0ms

bsearch59.0ms

simplify3.0ms

end0.0ms

sample3.2s

Profiling