Details

analyze107.0ms

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

sample27.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5141	26

prune7.0ms

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: 0.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-r_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(.f64 3 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 3 (.f64 v v))
3.0ms	(*.f64 PI.f64 t)
24.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
43.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5564	1795

prune166.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.3b

Counts

107 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 3)
0.2b	(*.f64 PI.f64 t)
0.4b	(.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (*.f64 PI.f64 t))
0.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 5 (.f64 v v)) (.f64 5 (.f64 v v)))) (.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (.f64 PI.f64 t))) (+.f64 1 (.f64 5 (.f64 v v)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
34×	`associate-*l/_binary64`
28×	`associate-*r/_binary64` `frac-times_binary64`
26×	`associate-/r/_binary64`
20×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
17×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-l_binary64`
7×	`pow-prod-down_binary64` `associate-r_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 116

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 3)
4.0ms	(*.f64 PI.f64 t)
12.0ms	(.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (*.f64 PI.f64 t))
34.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 5 (.f64 v v)) (.f64 5 (.f64 v v)))) (.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (.f64 PI.f64 t))) (+.f64 1 (.f64 5 (.f64 v v)))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (.f64 v v) 3)
3.0ms	(*.f64 PI.f64 t)
29.0ms	(.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (*.f64 PI.f64 t))
47.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 5 (.f64 v v)) (.f64 5 (.f64 v v)))) (.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))) (.f64 PI.f64 t))) (+.f64 1 (.f64 5 (.f64 v v)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4992	2956
1	4992	2956

prune245.0ms

Filtered

92 candidates to 128 candidates (-39.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Merged error: 0.3b

Counts

138 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 3)
0.3b	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))
0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))) (-.f64 1 (*.f64 v v))))
0.5b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-r_binary64` `associate-/r/_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 96

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 3)
10.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))
20.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))) (-.f64 1 (*.f64 v v))))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (.f64 v v) 3)
26.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))
39.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))) (-.f64 1 (*.f64 v v))))
21.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4970	2016
1	4970	2016

prune162.0ms

Filtered

79 candidates to 108 candidates (-36.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	107	11	118

Merged error: 0.3b

Counts

118 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
15×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
7×	`sqrt-prod_binary64`
6×	`pow-prod-down_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `frac-times_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-*l/_binary64`
1×	`associate-/r_binary64` `associate-l_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

14.0ms	(.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
25.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))
1.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series63.0ms

Counts

4 → 8

Calls

4 calls:

23.0ms	(.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
40.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (sqrt.f64 PI.f64) (.f64 t (sqrt.f64 PI.f64))) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify41.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5523	1831

prune100.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	96	11	107

Merged error: 0.3b

Counts

107 → 11

regimes265.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	42
1	92	42

end0.0ms

sample683.0ms

Algorithm

intervals

Results

539.0ms	8000×	body	80	valid
1.0ms	14×	body	80	nan

Details

analyze107.0ms

sample27.0ms

simplify41.0ms

prune7.0ms

localize15.0ms

rewrite42.0ms

series73.0ms

simplify38.0ms

prune166.0ms

localize20.0ms

rewrite62.0ms

series83.0ms

simplify82.0ms

prune245.0ms

localize17.0ms

rewrite48.0ms

series91.0ms

simplify38.0ms

prune162.0ms

localize17.0ms

rewrite45.0ms

series63.0ms

simplify41.0ms

prune100.0ms

regimes265.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample683.0ms

Profiling