Details

analyze4.0ms

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

12.0ms

256×

body

valid

simplify149.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4892	11
1	4892	11

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x)
0.0b	(log.f64 (/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x))
0.0b	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64` `times-frac_binary64`
22×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`
9×	`add-exp-log_binary64`
8×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `log-div_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 88

Calls

4 calls:

12.0ms	(/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x)
7.0ms	(log.f64 (/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x))
6.0ms	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x)
15.0ms	(log.f64 (/.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x)))) x))
5.0ms	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
6.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))

simplify31.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4999	1479
1	4999	1479

prune103.0ms

Filtered

77 candidates to 100 candidates (-29.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	1	101

Merged error: 0b

Counts

101 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
1.0b	(.f64 (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (.f64 x x))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod_binary64`
30×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`swap-sqr_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
7×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`flip3--_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
3.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
18.0ms	(.f64 (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (.f64 x x))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))
5.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
6.0ms	(sqrt.f64 (-.f64 1.0 (*.f64 x x)))
5.0ms	(.f64 (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (.f64 x x))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (-.f64 1.0 (*.f64 x x))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5046	1408

prune161.0ms

Filtered

74 candidates to 118 candidates (-59.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	118	1	119

Merged error: 0b

Counts

119 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	22
1	29	22

end0.0ms

sample488.0ms

Algorithm

intervals

Results

395.0ms	8000×	body	80	valid
0.0ms	5×	body	80	nan

Details

analyze4.0ms

sample18.0ms

simplify149.0ms

prune5.0ms

localize8.0ms

rewrite30.0ms

series32.0ms

simplify31.0ms

prune103.0ms

localize10.0ms

rewrite34.0ms

series21.0ms

simplify39.0ms

prune161.0ms

simplify2.0ms

end0.0ms

sample488.0ms

Profiling