Details

analyze694.0ms

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

sample52.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
10.0ms	146×	body	80	nan
9.0ms	162×	body	80	invalid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5189	17

prune4.0ms

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: 0.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 t t) 2.0)
0.0b	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
0.2b	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

5.0ms	(/.f64 (*.f64 t t) 2.0)
13.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
9.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

series74.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/.f64 (*.f64 t t) 2.0)
50.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
20.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4965	861
1	4965	861

prune113.0ms

Filtered

52 candidates to 71 candidates (-36.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 0.0b

Counts

72 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
0.0b	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))))
0.2b	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1_binary64`
38×	`add-exp-log_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`pow-prod-down_binary64`
23×	`cbrt-unprod_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
19×	`cbrt-prod_binary64`
17×	`associate-r_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`associate-*l/_binary64`
11×	`associate-l_binary64`
6×	`swap-sqr_binary64` `pow1/3_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow-plus_binary64` `sqrt-prod_binary64` `pow2_binary64`

Counts

4 → 117

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
22.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
18.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))))
10.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
71.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
109.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 t t) 2.0))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))))
20.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	2090
1	4975	2090

prune196.0ms

Filtered

85 candidates to 129 candidates (-51.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 0.0b

Counts

139 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (.f64 t t) 2.0)) 2/3)) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
0.0b	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)) 2/3))
0.2b	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))
18.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (.f64 t t) 2.0)) 2/3)) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
13.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)) 2/3))
10.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)))
52.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (.f64 t t) 2.0)) 2/3)) (cbrt.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0))))
106.0ms	(.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (.f64 z 2.0))) (pow.f64 (exp.f64 (/.f64 (*.f64 t t) 2.0)) 2/3))
18.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 (*.f64 z 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5060	1574

prune137.0ms

Filtered

68 candidates to 98 candidates (-44.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Merged error: 0.0b

Counts

108 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 t t) 2.0)
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0)) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
0.2b	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z))
0.5b	(.f64 (.f64 (-.f64 (*.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
20×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
12×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l/_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`pow-prod-down_binary64`
7×	`sqrt-prod_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(/.f64 (*.f64 t t) 2.0)
17.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0)) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
8.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z))
11.0ms	(.f64 (.f64 (-.f64 (*.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0))

series95.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (*.f64 t t) 2.0)
57.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0)) (exp.f64 (/.f64 (*.f64 t t) 2.0)))
13.0ms	(.f64 (-.f64 (.f64 x 0.5) y) (sqrt.f64 z))
21.0ms	(.f64 (.f64 (-.f64 (*.f64 x 0.5) y) (sqrt.f64 z)) (sqrt.f64 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4973	1257
1	4973	1257

prune93.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 0b

Counts

113 → 8

regimes837.0ms

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	34	27
1	34	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

547.0ms	6199×	body	80	invalid
454.0ms	8000×	body	80	valid
253.0ms	4560×	body	80	nan

Details

analyze694.0ms

sample52.0ms

simplify88.0ms

prune4.0ms

localize12.0ms

rewrite29.0ms

series74.0ms

simplify62.0ms

prune113.0ms

localize16.0ms

rewrite62.0ms

series231.0ms

simplify67.0ms

prune196.0ms

localize18.0ms

rewrite47.0ms

series198.0ms

simplify72.0ms

prune137.0ms

localize13.0ms

rewrite43.0ms

series95.0ms

simplify56.0ms

prune93.0ms

regimes837.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling