Details

analyze5.0ms (0.3%)

Algorithm

1×

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample19.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify116.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5574	20

prune3.0ms (0.1%)

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

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

rewrite53.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

31.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series188.0ms (10.2%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
57.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
43.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify71.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4912	1919
1	4912	1919

prune115.0ms (6.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	1	100

Merged error: 0b

Counts

100 → 1

Compiler

Compiled 2144 to 1393 computations (35% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `associate-l_binary64`
4×	`distribute-lft-out_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `difference-of-squares_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 71

Calls

3 calls:

16.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
7.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series126.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

50.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
42.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
34.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify84.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4886	1402
1	4886	1402

prune82.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	2	81

Merged error: 0b

Counts

81 → 2

Compiler

Compiled 1510 to 1066 computations (29.4% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

rewrite26.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64` `sqrt-prod_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
4×	`pow1_binary64`
3×	`associate-/r*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `difference-of-squares_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 67

Calls

3 calls:

10.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
7.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series130.0ms (7%)

Counts

3 → 9

Calls

3 calls:

58.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
42.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
30.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify65.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5177	1462

prune79.0ms (4.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	76	2	78

Merged error: 0b

Counts

78 → 2

Compiler

Compiled 1363 to 915 computations (32.9% saved)

regimes8.0ms (0.4%)

Compiler: Compiled 26 to 22 computations (15.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms (0%)

sample620.0ms (33.5%)

Algorithm

1×

intervals

Results

441.0ms	8000×	body	128	valid
0.0ms	5×	body	128	nan

Compiler

Compiled 49 to 41 computations (16.3% saved)

Details

analyze5.0ms (0.3%)

sample19.0ms (1%)

simplify116.0ms (6.3%)

prune3.0ms (0.1%)

localize9.0ms (0.5%)

rewrite53.0ms (2.9%)

series188.0ms (10.2%)

simplify71.0ms (3.9%)

prune115.0ms (6.2%)

localize9.0ms (0.5%)

rewrite33.0ms (1.8%)

series126.0ms (6.8%)

simplify84.0ms (4.5%)

prune82.0ms (4.5%)

localize8.0ms (0.4%)

rewrite26.0ms (1.4%)

series130.0ms (7%)

simplify65.0ms (3.5%)

prune79.0ms (4.3%)

regimes8.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample620.0ms (33.5%)

Profiling