Details

analyze78.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample22.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid
1.0ms	11×	body	80	nan

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	1050	21
1	1050	21

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.1b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.1b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
0.2b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
26×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
15×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
8×	`associate-*r/_binary64` `sqrt-prod_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64` `sqrt-div_binary64`
5×	`prod-exp_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `div-exp_binary64` `pow-flip_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate-l/_binary64`
2×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64`

Counts

4 → 126

Calls

4 calls:

13.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
16.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
11.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
18.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
66.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
32.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5436	2813

prune189.0ms

Filtered

108 candidates to 138 candidates (-27.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	7	140

Merged error: 0b

Counts

140 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
0.2b	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
0.2b	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
16×	`associate-l_binary64`
14×	`associate-r_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`prod-exp_binary64`
6×	`difference-of-squares_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `flip--_binary64` `frac-times_binary64` `pow-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 100

Calls

4 calls:

10.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))
12.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
11.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
6.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

series161.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))
45.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
28.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
68.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

simplify98.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4937	2163
1	4937	2163

prune145.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	113	6	119

Merged error: 0b

Counts

119 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9 (-.f64 a 1/3))
0.2b	(pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)
0.2b	(.f64 rand (pow.f64 (.f64 9 (-.f64 a 1/3)) -1/2))
9.5b	(.f64 (-.f64 a 1/3) (.f64 rand (pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`prod-exp_binary64`
14×	`*-un-lft-identity_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
10×	`add-cube-cbrt_binary64`
6×	`pow-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `pow-pow_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate-l/_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 88

Calls

4 calls:

7.0ms	(*.f64 9 (-.f64 a 1/3))
6.0ms	(pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)
6.0ms	(.f64 rand (pow.f64 (.f64 9 (-.f64 a 1/3)) -1/2))
10.0ms	(.f64 (-.f64 a 1/3) (.f64 rand (pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 9 (-.f64 a 1/3))
30.0ms	(pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)
68.0ms	(.f64 rand (pow.f64 (.f64 9 (-.f64 a 1/3)) -1/2))
62.0ms	(.f64 (-.f64 a 1/3) (.f64 rand (pow.f64 (*.f64 9 (-.f64 a 1/3)) -1/2)))

simplify97.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4912	1752
1	4912	1752

prune101.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Merged error: 0b

Counts

106 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
60×	`sqrt-prod_binary64`
52×	`add-cube-cbrt_binary64`
33×	`associate-r_binary64`
30×	`add-exp-log_binary64` `associate-l_binary64`
20×	`add-cbrt-cube_binary64`
16×	`unswap-sqr_binary64`
11×	`difference-of-squares_binary64`
10×	`distribute-lft-out--_binary64`
9×	`pow1_binary64` `prod-exp_binary64` `div-exp_binary64`
8×	`associate-/r*_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
5×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 190

Calls

4 calls:

3.0ms	(sqrt.f64 (-.f64 a 1/3))
13.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
27.0ms	(*.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt.f64 (-.f64 a 1/3))
45.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
58.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
62.0ms	(*.f64 (/.f64 1 (sqrt.f64 9)) (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))

simplify88.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5019	4045

prune222.0ms

Filtered

140 candidates to 202 candidates (-44.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	203	5	208

Merged error: 0b

Counts

208 → 5

regimes28.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	25
1	26	25

end0.0ms

sample609.0ms

Algorithm

intervals

Results

447.0ms	8000×	body	80	valid
14.0ms	262×	body	80	invalid
14.0ms	266×	body	80	nan

Details

analyze78.0ms

sample22.0ms

simplify97.0ms

prune4.0ms

localize11.0ms

rewrite52.0ms

series155.0ms

simplify70.0ms

prune189.0ms

localize13.0ms

rewrite43.0ms

series161.0ms

simplify98.0ms

prune145.0ms

localize15.0ms

rewrite31.0ms

series179.0ms

simplify97.0ms

prune101.0ms

localize13.0ms

rewrite58.0ms

series182.0ms

simplify88.0ms

prune222.0ms

regimes28.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample609.0ms

Profiling