Details

analyze9.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample77.0ms

Algorithm

intervals

Results

64.0ms	256×	body	80	valid
3.0ms	261×	pre	80	true
1.0ms	5×	body	80	invalid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5067	34

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.4b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.4b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
22×	`associate-l_binary64`
18×	`frac-add_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

67.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
7.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
3.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series153.0ms

Counts

4 → 10

Calls

4 calls:

126.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
17.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
9.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

simplify66.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5616	3722

prune311.0ms

Filtered

97 candidates to 141 candidates (-45.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	126	15	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	15	143

Merged error: 0.7b

Counts

143 → 15

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac_binary64`
86×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`
46×	`associate-l_binary64`
44×	`unpow-prod-down_binary64`
18×	`frac-add_binary64`
17×	`add-exp-log_binary64`
16×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-r/_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `div-inv_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_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` `-commutative_binary64`

Counts

4 → 195

Calls

4 calls:

70.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
6.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series206.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
35.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
31.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify62.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5475	5571

prune395.0ms

Filtered

130 candidates to 205 candidates (-57.7%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	185	20	205
Fresh	10	4	14
Picked	0	1	1
Done	0	0	0
Total	195	25	220

Merged error: 0.2b

Counts

220 → 25

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`pow1_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`div-exp_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `prod-exp_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 79

Calls

4 calls:

12.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
3.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series61.0ms

Counts

4 → 8

Calls

4 calls:

35.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
27.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify52.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5027	656

prune163.0ms

Filtered

53 candidates to 87 candidates (-64.2%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	3	20	23
Picked	0	1	1
Done	0	1	1
Total	88	24	112

Merged error: 0.2b

Counts

112 → 24

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow_binary64` `add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`pow1_binary64` `pow-pow_binary64`
6×	`unpow-prod-down_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 86

Calls

4 calls:

5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series62.0ms

Counts

4 → 8

Calls

4 calls:

30.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
32.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify67.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4985	708
1	4985	708

prune152.0ms

Filtered

71 candidates to 94 candidates (-32.4%)

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	2	19	21
Picked	0	1	1
Done	0	2	2
Total	93	25	118

Merged error: 0.2b

Counts

118 → 25

regimes245.0ms

Accuracy

0% (1.0b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	35
1	30	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
99.0ms	8112×	pre	80	true
25.0ms	112×	body	80	invalid

Details

analyze9.0ms

sample77.0ms

simplify106.0ms

prune11.0ms

localize28.0ms

rewrite84.0ms

series153.0ms

simplify66.0ms

prune311.0ms

localize29.0ms

rewrite91.0ms

series206.0ms

simplify62.0ms

prune395.0ms

localize33.0ms

rewrite21.0ms

series61.0ms

simplify52.0ms

prune163.0ms

localize33.0ms

rewrite15.0ms

series62.0ms

simplify67.0ms

prune152.0ms

regimes245.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling