Details

analyze264.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample56.0ms

Algorithm

intervals

Results

17.0ms	91×	body	2560	nan
14.0ms	72×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	39×	body	640	nan
1.0ms	14×	body	320	nan
0.0ms	5×	body	160	nan
0.0ms	9×	body	80	nan

simplify161.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	5030	9

prune2.0ms

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: 28.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
26.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`sqrt-prod_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64` `log-div_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 45

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series20.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
4.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify56.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4991	599
1	4991	599

prune35.0ms

Filtered

43 candidates to 54 candidates (-25.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0b

Counts

55 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 x 1))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64`
16×	`sqrt-div_binary64`
10×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 x 1))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
3.0ms	(sqrt.f64 (+.f64 x 1))
14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 x 1))
6.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
4.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

simplify56.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4888	1128
1	4888	1128

prune61.0ms

Filtered

76 candidates to 101 candidates (-32.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	2	103

Merged error: 0b

Counts

103 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))
0.2b	(/.f64 1/4 (*.f64 x x))
0.2b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.4b	(/.f64 3/32 (pow.f64 x 4))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
13×	`add-log-exp_binary64`
12×	`unpow-prod-down_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
9×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64`
7×	`log-pow_binary64`
6×	`associate-/l*_binary64`
5×	`diff-log_binary64` `div-exp_binary64`
4×	`sqr-pow_binary64` `sum-log_binary64`
3×	`log-prod_binary64` `cbrt-undiv_binary64` `associate--l+_binary64`
2×	`sub-neg_binary64` `associate-+r-_binary64` `flip3--_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `pow-exp_binary64`

Counts

4 → 112

Calls

4 calls:

36.0ms	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))
8.0ms	(/.f64 1/4 (*.f64 x x))
30.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
5.0ms	(/.f64 3/32 (pow.f64 x 4))

series41.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))
5.0ms	(/.f64 1/4 (*.f64 x x))
15.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
10.0ms	(/.f64 3/32 (pow.f64 x 4))

simplify32.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5055	1637

prune69.0ms

Filtered

79 candidates to 124 candidates (-57.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	124	2	126

Merged error: 0b

Counts

126 → 2

regimes15.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

591.0ms	3002×	body	2560	nan
401.0ms	2500×	body	1280	nan
321.0ms	8000×	body	80	valid
169.0ms	1314×	body	640	nan
59.0ms	612×	body	320	nan
22.0ms	324×	body	160	nan
10.0ms	291×	body	80	nan

Details

analyze264.0ms

sample56.0ms

simplify161.0ms

prune2.0ms

localize7.0ms

rewrite20.0ms

series20.0ms

simplify56.0ms

prune35.0ms

localize9.0ms

rewrite27.0ms

series23.0ms

simplify56.0ms

prune61.0ms

localize12.0ms

rewrite85.0ms

series41.0ms

simplify32.0ms

prune69.0ms

regimes15.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling