Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample18.0ms

Algorithm

intervals

Results

13.0ms

256×

body

128

valid

simplify293.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (281.0ms)

Iter	Nodes	Cost
0	7544	20

prune1.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
16×	`distribute-lft-out_binary64`
15×	`log-prod_binary64`
13×	`div-inv_binary64`
10×	`difference-of-squares_binary64`
8×	`associate-/l*_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-rgt-out_binary64` `add-cbrt-cube_binary64`
4×	`sqrt-div_binary64`
3×	`associate-/r*_binary64` `log-div_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `frac-add_binary64` `distribute-rgt1-in_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 117

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
26.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
25.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
52.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
41.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
101.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5222	2730

prune106.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Merged error: 0b

Counts

130 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
0.0b	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
0.2b	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.2b	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
72×	`sqrt-prod_binary64`
52×	`times-frac_binary64`
40×	`add-sqr-sqrt_binary64`
36×	`log-prod_binary64`
32×	`distribute-lft-out_binary64`
26×	`add-cube-cbrt_binary64`
24×	`div-inv_binary64`
12×	`distribute-rgt-out_binary64` `sqrt-div_binary64`
10×	`pow1_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64` `log-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `frac-add_binary64` `add-cbrt-cube_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`rem-log-exp_binary64` `rem-sqrt-square_binary64`

Counts

4 → 120

Calls

4 calls:

30.0ms	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
27.0ms	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
26.0ms	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
29.0ms	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
138.0ms	(log.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
80.0ms	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
80.0ms	(sqrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5118	3872

prune161.0ms

Filtered

84 candidates to 132 candidates (-57.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	2	134

Merged error: 0b

Counts

134 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.6b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))
0.7b	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`log-prod_binary64`
14×	`cbrt-prod_binary64`
13×	`times-frac_binary64`
11×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `div-inv_binary64`
5×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `distribute-rgt-out_binary64` `log-div_binary64`
2×	`sqr-pow_binary64` `difference-of-squares_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `frac-add_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 92

Calls

4 calls:

3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
26.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
3.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))
3.0ms	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)

series391.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
94.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
97.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))
157.0ms	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)

simplify86.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4926	2771
1	4926	2771

prune82.0ms

Filtered

63 candidates to 104 candidates (-65.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	104	2	106

Merged error: 0b

Counts

106 → 2

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	46
1	31	46

end0.0ms

sample505.0ms

Algorithm

intervals

Results

408.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Details

analyze5.0ms

sample18.0ms

simplify293.0ms

prune1.0ms

localize10.0ms

rewrite77.0ms

series273.0ms

simplify82.0ms

prune106.0ms

localize12.0ms

rewrite129.0ms

series428.0ms

simplify88.0ms

prune161.0ms

localize14.0ms

rewrite44.0ms

series391.0ms

simplify86.0ms

prune82.0ms

regimes35.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample505.0ms

Profiling