Details

analyze742.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

sample53.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
12.0ms	209×	body	80	invalid
7.0ms	129×	body	80	nan

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4911	16
1	4911	16

prune11.0ms

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: 0.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`associate-r_binary64`
12×	`unpow-prod-down_binary64`
11×	`add-cbrt-cube_binary64`
10×	`prod-exp_binary64` `sqrt-prod_binary64`
9×	`pow1_binary64`
8×	`sqrt-pow1_binary64`
6×	`pow-pow_binary64` `associate-*l/_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `sqr-pow_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `sqrt-pow2_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64`

Counts

4 → 92

Calls

4 calls:

4.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
3.0ms	(sqrt.f64 (exp.f64 t))
14.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
10.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
3.0ms	(sqrt.f64 (exp.f64 t))
64.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
16.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

simplify83.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4958	1122
1	4958	1122

prune127.0ms

Filtered

71 candidates to 104 candidates (-46.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.5b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
22×	`associate-r_binary64` `prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64` `associate-*l/_binary64`
10×	`cbrt-unprod_binary64`
6×	`unpow-prod-down_binary64`
5×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `exp-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64`

Counts

4 → 96

Calls

4 calls:

2.0ms	(sqrt.f64 (exp.f64 t))
16.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
11.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

series104.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt.f64 (exp.f64 t))
69.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
19.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4969	1323
1	4969	1323

prune129.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	107	10	117

Merged error: 0b

Counts

117 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-exp-log_binary64`
79×	`prod-exp_binary64`
41×	`cbrt-unprod_binary64`
39×	`add-cbrt-cube_binary64`
36×	`pow1_binary64`
26×	`associate-r_binary64`
22×	`pow-prod-down_binary64`
20×	`associate-*l/_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`sqrt-prod_binary64`
6×	`pow-to-exp_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cbrt-prod_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sqr-pow_binary64`

Counts

4 → 128

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
15.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
20.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
45.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
19.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

simplify71.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	2094
1	4959	2094

prune140.0ms

Filtered

75 candidates to 140 candidates (-86.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	140	10	150

Merged error: 0b

Counts

150 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.3b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
40×	`prod-exp_binary64`
34×	`associate-r_binary64` `add-cbrt-cube_binary64`
25×	`sqrt-prod_binary64`
20×	`pow1_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `associate-*l/_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64`
6×	`associate-l_binary64` `unpow-prod-down_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sqr-pow_binary64`

Counts

4 → 116

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
13.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
17.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
13.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
20.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
19.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4968	1793
1	4968	1793

prune103.0ms

Filtered

76 candidates to 128 candidates (-68.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	128	10	138

Merged error: 0b

Counts

138 → 10

regimes748.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

455.0ms	8000×	body	80	valid
342.0ms	5978×	body	80	invalid
253.0ms	4449×	body	80	nan

Details

analyze742.0ms

sample53.0ms

simplify118.0ms

prune11.0ms

localize13.0ms

rewrite33.0ms

series88.0ms

simplify83.0ms

prune127.0ms

localize14.0ms

rewrite41.0ms

series104.0ms

simplify64.0ms

prune129.0ms

localize18.0ms

rewrite79.0ms

series146.0ms

simplify71.0ms

prune140.0ms

localize17.0ms

rewrite69.0ms

series120.0ms

simplify68.0ms

prune103.0ms

regimes748.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling