Details

analyze2.5s

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

sample50.0ms

Algorithm

intervals

Results

26.0ms	254×	body	80	valid
2.0ms	3×	body	1280	invalid
2.0ms	4×	body	640	invalid
2.0ms	15×	body	80	invalid
2.0ms	5×	body	320	invalid
1.0ms	1×	body	2560	invalid
0.0ms	2×	body	160	invalid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5362	28

prune15.0ms

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: 13.8b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite37.0ms

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:

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

series65.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
7.0ms	(*.f64 K (+.f64 m n))
18.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
24.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify34.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4936	801
1	4936	801

prune96.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 0.4b

Counts

79 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

0.0b

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64` `exp-prod_binary64`
5×	`distribute-lft-out--_binary64`
4×	`pow1_binary64` `diff-log_binary64` `add-exp-log_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `add-cbrt-cube_binary64` `rem-exp-log_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `associate--r+_binary64` `flip3--_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `exp-diff_binary64` `exp-sum_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

3 → 55

Calls

3 calls:

18.0ms

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

17.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

11.0ms

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

series119.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms

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

60.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

16.0ms

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

simplify35.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5238	1009

prune75.0ms

Filtered

44 candidates to 64 candidates (-45.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.4b

Counts

68 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite30.0ms

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×	`sub-neg_binary64` `cos-diff_binary64` `cos-sum_binary64` `cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 38

Calls

4 calls:

2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series148.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
24.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
24.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
26.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify62.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4846	612
1	4846	612

prune86.0ms

Filtered

41 candidates to 50 candidates (-22.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	50	4	54

Merged error: 0.4b

Counts

54 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n))))
8.1b	(sqrt.f64 (*.f64 K (+.f64 m n)))
8.1b	(sqrt.f64 (*.f64 K (+.f64 m n)))
15.6b	(cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1_binary64`
32×	`sqrt-pow1_binary64`
22×	`pow-prod-down_binary64`
18×	`associate-*r/_binary64`
16×	`sqrt-div_binary64`
12×	`pow1/2_binary64`
10×	`pow-prod-up_binary64` `add-sqr-sqrt_binary64`
8×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `flip-+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `pow-sqr_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`sub-neg_binary64` `cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `prod-exp_binary64` `cos-sum_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n))))
5.0ms	(sqrt.f64 (*.f64 K (+.f64 m n)))
5.0ms	(sqrt.f64 (*.f64 K (+.f64 m n)))
16.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

series68.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n))))
17.0ms	(sqrt.f64 (*.f64 K (+.f64 m n)))
18.0ms	(sqrt.f64 (*.f64 K (+.f64 m n)))
25.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

simplify48.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5085	863

prune87.0ms

Filtered

61 candidates to 104 candidates (-70.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	104	4	108

Merged error: 0.4b

Counts

108 → 4

regimes337.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

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

822.0ms	7817×	body	80	valid
56.0ms	89×	body	1280	invalid
37.0ms	81×	body	640	invalid
34.0ms	297×	body	80	invalid
32.0ms	74×	body	640	valid
27.0ms	43×	body	1280	valid
20.0ms	64×	body	320	invalid
13.0ms	43×	body	320	valid
7.0ms	33×	body	160	invalid
5.0ms	23×	body	160	valid
5.0ms	3×	body	2560	invalid

Details

analyze2.5s

sample50.0ms

simplify38.0ms

prune15.0ms

localize21.0ms

rewrite37.0ms

series65.0ms

simplify34.0ms

prune96.0ms

localize13.0ms

rewrite47.0ms

series119.0ms

simplify35.0ms

prune75.0ms

localize25.0ms

rewrite30.0ms

series148.0ms

simplify62.0ms

prune86.0ms

localize21.0ms

rewrite45.0ms

series68.0ms

simplify48.0ms

prune87.0ms

regimes337.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling