Details

analyze51.0ms

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample24.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	1×	body	80	invalid

simplify200.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (196.0ms)

Iter	Nodes	Cost
0	4819	14
1	4819	14

prune3.0ms

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: 0.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
0.2b	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `associate-l_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
14.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))
6.0ms	(*.f64 3.0 (sqrt.f64 x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
16.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))
6.0ms	(*.f64 3.0 (sqrt.f64 x))

simplify34.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5384	938

prune129.0ms

Filtered

65 candidates to 94 candidates (-44.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.0b

Counts

95 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))
0.2b	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1.0 x) 9.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`div-inv_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 131

Calls

4 calls:

14.0ms	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))
23.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
8.0ms	(*.f64 3.0 (sqrt.f64 x))
7.0ms	(/.f64 (/.f64 1.0 x) 9.0)

series28.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))
15.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
3.0ms	(/.f64 (/.f64 1.0 x) 9.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5548	1567

prune188.0ms

Filtered

110 candidates to 143 candidates (-30.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1.0 (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))
0.3b	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

353×	`times-frac_binary64`
257×	`add-sqr-sqrt_binary64`
192×	`*-un-lft-identity_binary64`
184×	`add-cube-cbrt_binary64`
109×	`sqrt-prod_binary64`
70×	`associate-r_binary64`
54×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
28×	`associate-/l*_binary64`
24×	`div-exp_binary64`
22×	`associate-l_binary64`
20×	`unswap-sqr_binary64`
15×	`associate-/r*_binary64`
14×	`cbrt-undiv_binary64`
12×	`prod-exp_binary64` `div-inv_binary64`
8×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 332

Calls

4 calls:

5.0ms	(/.f64 1.0 (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))
48.0ms	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))
10.0ms	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 1.0 (sqrt.f64 x))
9.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))
17.0ms	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5056	3851

prune593.0ms

Filtered

215 candidates to 344 candidates (-60.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	344	10	354

Merged error: 0.0b

Counts

354 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.4b	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow1_binary64`
28×	`sqrt-pow1_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`pow-prod-down_binary64`
16×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`sqrt-prod_binary64`
10×	`pow1/2_binary64` `pow-prod-up_binary64` `associate-l_binary64`
6×	`pow-sqr_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/.f64 1.0 (*.f64 x 9.0))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
12.0ms	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 1.0 (*.f64 x 9.0))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
11.0ms	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4944	753
1	4944	753

prune108.0ms

Filtered

73 candidates to 126 candidates (-72.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	126	10	136

Merged error: 0.0b

Counts

136 → 10

regimes115.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	16
1	28	16

end0.0ms

sample478.0ms

Algorithm

intervals

Results

338.0ms	8000×	body	80	valid
9.0ms	144×	body	80	nan
3.0ms	85×	body	80	invalid

Details

analyze51.0ms

sample24.0ms

simplify200.0ms

prune3.0ms

localize9.0ms

rewrite32.0ms

series32.0ms

simplify34.0ms

prune129.0ms

localize9.0ms

rewrite56.0ms

series28.0ms

simplify41.0ms

prune188.0ms

localize12.0ms

rewrite86.0ms

series41.0ms

simplify110.0ms

prune593.0ms

localize13.0ms

rewrite32.0ms

series24.0ms

simplify84.0ms

prune108.0ms

regimes115.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample478.0ms

Profiling