Details

analyze432.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample39.0ms

Algorithm

intervals

Results

11.0ms	178×	body	80	valid
8.0ms	31×	body	2560	valid
4.0ms	17×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	18×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	10×	body	80	invalid
0.0ms	5×	body	160	valid

simplify614.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	715	20
1	715	20

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: 32.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
27.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
55.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
74.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4936	2470
1	4936	2470

prune97.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Merged error: 6.6b

Counts

102 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 175

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
29.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
63.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5112	5825

prune106.0ms

Filtered

103 candidates to 187 candidates (-81.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	187	8	195

Merged error: 6.6b

Counts

195 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
16.2b	(/.f64 (*.f64 a c) a)
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
64.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(/.f64 (*.f64 a c) a)
57.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4855	967
1	4855	967

prune52.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	74	8	82

Merged error: 6.6b

Counts

82 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-rgt-neg-in_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

10.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
60.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5693	1819

prune50.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	90	8	98

Merged error: 6.6b

Counts

98 → 8

regimes182.0ms

Accuracy

95% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.3b

bsearch75.0ms

Steps

Iters	Range		Point
9	2.9275797170266654e+65	3.737701949375755e+73	3.365943335282884e+73
1	9.197852207191395e-256	9.704886006586613e-256	9.324610657040199e-256
10	-4.017204298093521e+88	-6.843620271520313e+76	-3.7135256748667976e+88

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	79
1	118	79

end0.0ms

sample1.1s

Algorithm

intervals

Results

274.0ms	1083×	body	2560	valid
232.0ms	5099×	body	80	valid
185.0ms	898×	body	1280	valid
75.0ms	439×	body	640	valid
34.0ms	110×	body	5120	valid
33.0ms	786×	body	80	nan
30.0ms	230×	body	320	valid
12.0ms	141×	body	160	valid
10.0ms	233×	body	80	invalid

Details

analyze432.0ms

sample39.0ms

simplify614.0ms

prune3.0ms

localize11.0ms

rewrite34.0ms

series229.0ms

simplify102.0ms

prune97.0ms

localize10.0ms

rewrite43.0ms

series261.0ms

simplify108.0ms

prune106.0ms

localize10.0ms

rewrite22.0ms

series160.0ms

simplify94.0ms

prune52.0ms

localize9.0ms

rewrite28.0ms

series317.0ms

simplify98.0ms

prune50.0ms

regimes182.0ms

bsearch75.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling