Details

analyze764.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample39.0ms

Algorithm

intervals

Results

10.0ms	28×	body	2048	valid
9.0ms	189×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	18×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	7×	body	512	valid
0.0ms	3×	body	256	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.1b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
41.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
79.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
57.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4926	2082
1	4926	2082

prune131.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	77	14	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	14	92

Merged error: 13.3b

Counts

92 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
0.9b	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `exp-sum_binary64`

Counts

4 → 55

Calls

4 calls:

7.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
17.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
9.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
73.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
135.0ms	(log.f64 (exp.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4946	1327
1	4946	1327

prune91.0ms

Filtered

59 candidates to 67 candidates (-13.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	67	14	81

Merged error: 13.3b

Counts

81 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3)
0.0b	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3))
0.9b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `cube-div_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 79

Calls

4 calls:

16.0ms	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3)
20.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3))
16.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3)
92.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))) 3))
81.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
50.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4926	2284
1	4926	2284

prune111.0ms

Filtered

66 candidates to 91 candidates (-37.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	90	15	105

Merged error: 13.3b

Counts

105 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
3.1b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
24×	`associate-r_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
14×	`sqrt-prod_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `prod-exp_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
17.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
61.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
87.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
49.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5169	1914

prune100.0ms

Filtered

71 candidates to 97 candidates (-36.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	96	16	112

Merged error: 13.3b

Counts

112 → 16

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	30
1	22	30

end0.0ms

sample1.1s

Algorithm

intervals

Results

295.0ms	6048×	body	128	valid
215.0ms	805×	body	2048	valid
132.0ms	8000×	pre	128	true
106.0ms	514×	body	1024	valid
91.0ms	274×	body	4096	valid
37.0ms	235×	body	512	valid
12.0ms	124×	body	256	valid

Details

analyze764.0ms

sample39.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite43.0ms

series242.0ms

simplify87.0ms

prune131.0ms

localize15.0ms

rewrite52.0ms

series294.0ms

simplify78.0ms

prune91.0ms

localize14.0ms

rewrite66.0ms

series445.0ms

simplify72.0ms

prune111.0ms

localize12.0ms

rewrite43.0ms

series243.0ms

simplify69.0ms

prune100.0ms

regimes89.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling