Details

analyze110.0ms

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
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

sample13.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

prune4.0ms

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: 0.0b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
2×	`associate-+l+_binary64`
1×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 13

Calls

1 calls:

7.0ms

(+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(+.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))

simplify53.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5191	187

prune17.0ms

Filtered

11 candidates to 16 candidates (-45.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Merged error: 0b

Counts

17 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))
0.6b	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.6b	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.6b	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

17.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))
6.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
6.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
6.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))
34.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
34.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
36.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4951	1793
1	4951	1793

prune96.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`
14×	`sqrt-div_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
8×	`add-log-exp_binary64` `swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`associate-+l+_binary64` `unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
9.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
7.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
18.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
6.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
7.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
7.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (*.f64 y y))))

simplify58.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4952	1406
1	4952	1406

prune57.0ms

Filtered

68 candidates to 110 candidates (-61.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Merged error: 0b

Counts

114 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))

0.5b

(-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))

26.6b

(/.f64 (-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
17×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`difference-of-squares_binary64`
14×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64`
8×	`cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64` `frac-times_binary64` `associate--l+_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `associate-*l/_binary64`
1×	`sub-neg_binary64` `swap-sqr_binary64` `diff-log_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

3 → 108

Calls

3 calls:

13.0ms

(*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))

16.0ms

(-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))

26.0ms

(/.f64 (-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))

series39.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms

(*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2)))

17.0ms

(-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4))

19.0ms

(/.f64 (-.f64 (*.f64 (*.f64 x (+.f64 x 2)) (*.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4948	1908
1	4948	1908

prune69.0ms

Filtered

69 candidates to 117 candidates (-69.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	117	4	121

Merged error: 0b

Counts

121 → 4

regimes75.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

end0.0ms

sample358.0ms

Algorithm

intervals

Results

234.0ms	8000×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze110.0ms

sample13.0ms

simplify6.0ms

prune4.0ms

localize5.0ms

rewrite7.0ms

series7.0ms

simplify53.0ms

prune17.0ms

localize9.0ms

rewrite39.0ms

series145.0ms

simplify53.0ms

prune96.0ms

localize8.0ms

rewrite44.0ms

series33.0ms

simplify58.0ms

prune57.0ms

localize10.0ms

rewrite59.0ms

series39.0ms

simplify53.0ms

prune69.0ms

regimes75.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample358.0ms

Profiling