Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample48.0ms

Algorithm

intervals

Results

26.0ms	252×	body	80	valid
2.0ms	4×	body	1280	invalid
1.0ms	3×	body	640	invalid
1.0ms	3×	body	320	valid
1.0ms	3×	body	320	invalid
1.0ms	7×	body	80	invalid
0.0ms	1×	body	160	valid
0.0ms	1×	body	160	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5362	28

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `prod-exp_binary64` `cos-sum_binary64` `times-frac_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

7.0ms	(*.f64 K (+.f64 m n))
9.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series61.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 K (+.f64 m n))
14.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify34.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4936	801
1	4936	801

prune66.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	2	79

Merged error: 0.8b

Counts

79 → 2

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64`
2×	`add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

2 → 33

Calls

2 calls:

16.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series52.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify25.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5500	476

prune32.0ms

Filtered

27 candidates to 39 candidates (-44.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Merged error: 0.8b

Counts

41 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
2.3b	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
8.0b	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
24.8b	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
10×	`log-prod_binary64`
9×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `unpow-prod-down_binary64`
5×	`exp-sum_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `log-div_binary64` `exp-prod_binary64`
3×	`pow-unpow_binary64` `distribute-lft-out--_binary64`
2×	`flip3--_binary64` `log-pow_binary64` `exp-diff_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `times-frac_binary64` `pow-exp_binary64`

Counts

4 → 63

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
11.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
14.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
25.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
23.0ms	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify29.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5272	944

prune59.0ms

Filtered

52 candidates to 75 candidates (-44.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Merged error: 0.8b

Counts

77 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

8.0b	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0b	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0b	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
24.7b	(cos.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod_binary64`
13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`log-div_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 55

Calls

4 calls:

9.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
4.0ms	(cos.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))

series849.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
25.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
29.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
769.0ms	(cos.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (log.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5078	1150

prune82.0ms

Filtered

50 candidates to 67 candidates (-34.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	67	3	70

Merged error: 0.8b

Counts

70 → 3

regimes246.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

839.0ms	7828×	body	80	valid
47.0ms	80×	body	1280	invalid
37.0ms	78×	body	640	invalid
30.0ms	67×	body	640	valid
29.0ms	47×	body	1280	valid
27.0ms	258×	body	80	invalid
17.0ms	56×	body	320	invalid
15.0ms	43×	body	320	valid
8.0ms	38×	body	160	invalid
3.0ms	15×	body	160	valid
3.0ms	3×	body	2560	invalid

Details

analyze2.4s

sample48.0ms

simplify39.0ms

prune13.0ms

localize21.0ms

rewrite38.0ms

series61.0ms

simplify34.0ms

prune66.0ms

localize16.0ms

rewrite28.0ms

series52.0ms

simplify25.0ms

prune32.0ms

localize22.0ms

rewrite44.0ms

series78.0ms

simplify29.0ms

prune59.0ms

localize30.0ms

rewrite35.0ms

series849.0ms

simplify78.0ms

prune82.0ms

regimes246.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling