Details

analyze52.0ms

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

sample17.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
0.0ms	3×	body	80	nan
0.0ms	1×	body	80	invalid

simplify161.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	1584	18
1	1584	18

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: 0.4b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
7×	`prod-exp_binary64`
6×	`distribute-lft-out--_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `difference-of-squares_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`sub-neg_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-inv_binary64` `associate--l+_binary64`
2×	`flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `-commutative_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `sum-log_binary64`

Counts

4 → 99

Calls

4 calls:

8.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
5.0ms	(/.f64 1 (*.f64 x 9))
13.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
10.0ms	(/.f64 1 (*.f64 x 9))
38.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
17.0ms	(*.f64 3 (sqrt.f64 x))

simplify77.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4948	1440
1	4948	1440

prune96.0ms

Filtered

67 candidates to 111 candidates (-65.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
0.4b	(/.f64 1/9 x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-*r/_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64` `associate-l_binary64` `times-frac_binary64`
6×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `frac-add_binary64` `flip-+_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `sum-log_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 100

Calls

4 calls:

10.0ms	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
14.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
17.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
3.0ms	(/.f64 1/9 x)

series91.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 (/.f64 1/9 x) (+.f64 y -1))
31.0ms	(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
39.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (/.f64 1/9 x) (+.f64 y -1))))
11.0ms	(/.f64 1/9 x)

simplify108.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4937	1800
1	4937	1800

prune100.0ms

Filtered

75 candidates to 112 candidates (-49.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1 x) 9))
0.2b	(/.f64 (/.f64 1 x) 9)
0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
14×	`associate-r_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `div-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`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 135

Calls

4 calls:

15.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
6.0ms	(/.f64 (/.f64 1 x) 9)
20.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))

series85.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
10.0ms	(/.f64 (/.f64 1 x) 9)
40.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
17.0ms	(*.f64 3 (sqrt.f64 x))

simplify87.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4933	2077
1	4933	2077

prune116.0ms

Filtered

94 candidates to 147 candidates (-56.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	147	11	158

Merged error: 0.0b

Counts

158 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) 9)
0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 x) 9)
19.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
10.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

series101.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 x) 9)
49.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
19.0ms	(*.f64 3 (sqrt.f64 x))
18.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

simplify62.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4930	2164
1	4930	2164

prune103.0ms

Filtered

94 candidates to 153 candidates (-62.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	153	11	164

Merged error: 0.0b

Counts

164 → 11

regimes48.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms

sample466.0ms

Algorithm

intervals

Results

327.0ms	8000×	body	80	valid
5.0ms	128×	body	80	nan
3.0ms	69×	body	80	invalid

Details

analyze52.0ms

sample17.0ms

simplify161.0ms

prune4.0ms

localize9.0ms

rewrite36.0ms

series77.0ms

simplify77.0ms

prune96.0ms

localize8.0ms

rewrite46.0ms

series91.0ms

simplify108.0ms

prune100.0ms

localize10.0ms

rewrite52.0ms

series85.0ms

simplify87.0ms

prune116.0ms

localize11.0ms

rewrite44.0ms

series101.0ms

simplify62.0ms

prune103.0ms

regimes48.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample466.0ms

Profiling