Details

analyze767.0ms

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample57.0ms

Algorithm

intervals

Results

14.0ms	53×	body	1024	valid
11.0ms	162×	body	128	valid
6.0ms	24×	body	1024	nan
4.0ms	19×	body	512	valid
3.0ms	44×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	19×	body	256	valid
2.0ms	12×	body	256	nan
1.0ms	3×	body	2048	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5188	41

prune2.0ms

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: 40.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.5b	(*.f64 (sqrt.f64 2) t)
13.2b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.9b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

21.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
5.0ms	(*.f64 (sqrt.f64 2) t)
16.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

830.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
52.0ms	(*.f64 (sqrt.f64 2) t)
322.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
1.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify49.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5200	3052

prune146.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 6.6b

Counts

92 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

2.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.7b	(/.f64 (*.f64 l l) x)
9.5b	(/.f64 (*.f64 t t) x)
25.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
23.0ms	(/.f64 (*.f64 l l) x)
23.0ms	(/.f64 (*.f64 t t) x)
171.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5094	1977

prune101.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	79	11	90

Merged error: 4.7b

Counts

90 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) t)
2.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.5b	(/.f64 (*.f64 t t) x)
25.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 2) t)
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(*.f64 (sqrt.f64 2) t)
82.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
24.0ms	(/.f64 (*.f64 t t) x)
179.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4976	1974
1	4976	1974

prune98.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	90	8	98

Merged error: 4.7b

Counts

98 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
2.6b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.5b	(/.f64 (*.f64 t t) x)
25.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
80.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
24.0ms	(/.f64 (*.f64 t t) x)
179.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4984	2011
1	4984	2011

prune92.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 4.7b

Counts

84 → 10

regimes235.0ms

Accuracy

77.1% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 27.6b

bsearch280.0ms

Steps

Iters	Range		Point
6	3.9890627528340063e+24	6.200770552515706e+25	6.081297735023138e+25
6	-1.2780350792048932e-244	-2.943921438694214e-245	-1.2658084059740561e-244
7	-1.5008820808456522e-161	-8.012301330118967e-164	-8.216739562820036e-164
5	-2.5298683298492165e+119	-7.943047251054198e+118	-2.4895486145830267e+119

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	153	271
1	153	271

end0.0ms

sample1.7s

Algorithm

intervals

Results

370.0ms	5351×	body	128	valid
319.0ms	1204×	body	1024	valid
211.0ms	808×	body	1024	nan
166.0ms	852×	body	512	valid
100.0ms	1511×	body	128	nan
99.0ms	528×	body	512	nan
72.0ms	527×	body	256	valid
32.0ms	259×	body	256	nan
22.0ms	66×	body	2048	valid

Details

analyze767.0ms

sample57.0ms

simplify86.0ms

prune2.0ms

localize17.0ms

rewrite67.0ms

series2.8s

simplify49.0ms

prune146.0ms

localize16.0ms

rewrite35.0ms

series301.0ms

simplify42.0ms

prune101.0ms

localize16.0ms

rewrite35.0ms

series336.0ms

simplify61.0ms

prune98.0ms

localize20.0ms

rewrite34.0ms

series335.0ms

simplify62.0ms

prune92.0ms

regimes235.0ms

bsearch280.0ms

simplify5.0ms

end0.0ms

sample1.7s

Profiling