Details

analyze12.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample228.0ms (6.6%)

Algorithm

1×

intervals

Results

217.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify130.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite170.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `associate-/r/_binary64` `associate-/r*_binary64`
3×	`add-log-exp_binary64`
2×	`div-inv_binary64` `associate-/l/_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

Compiler

Compiled 2038 to 1659 computations (18.6% saved)

series91.0ms (2.7%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

33.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
23.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 425 to 398 computations (6.4% saved)

simplify79.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6419	2047

prune131.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	2	118

Error

Counts

118 → 2

Compiler

Compiled 2022 to 1631 computations (19.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite295.0ms (8.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

123×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
23×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`cancel-sign-sub-inv_binary64`
16×	`distribute-lft-out--_binary64`
15×	`div-inv_binary64`
14×	`associate-/r/_binary64`
12×	`difference-of-squares_binary64` `distribute-rgt-out--_binary64`
10×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64` `associate-/r*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
4×	`sqrt-div_binary64`
3×	`div-exp_binary64`
2×	`frac-sub_binary64` `sub-div_binary64` `flip3--_binary64` `flip--_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 158

Calls

4 calls:

25.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
25.0ms	(sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x))))
8.0ms	(/.f64 1 (+.f64 1 x))
5.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 3758 to 2990 computations (20.4% saved)

series116.0ms (3.4%)

Error

Counts

4 → 28

Calls

4 calls:

31.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
25.0ms	(/.f64 x (+.f64 1 x))
22.0ms	(sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x))))
16.0ms	(/.f64 1 (+.f64 1 x))

Compiler

Compiled 822 to 731 computations (11.1% saved)

simplify95.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4934	2797
1	4934	2797

prune216.0ms (6.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	186	2	188

Error

Counts

188 → 2

Compiler

Compiled 3596 to 2877 computations (20% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite221.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

98×	`sqrt-prod_binary64`
91×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
11×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64` `associate-/l*_binary64`
8×	`sqrt-div_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
2×	`flip3--_binary64` `associate-/l/_binary64` `flip--_binary64` `flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
4.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
4.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 3038 to 2537 computations (16.5% saved)

series89.0ms (2.6%)

Error

Counts

4 → 21

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
18.0ms	(sqrt.f64 (-.f64 1 x))
18.0ms	(sqrt.f64 (+.f64 1 x))
17.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 635 to 563 computations (11.3% saved)

simplify112.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5646	3065

prune182.0ms (5.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	158	2	160

Error

Counts

160 → 2

Compiler

Compiled 2956 to 2448 computations (17.2% saved)

regimes214.0ms (6.3%)

Accuracy

Total 0.0b remaining (84.7%)

Threshold costs 0.0b (84.7%)

Compiler

Compiled 2223 to 1974 computations (11.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms (0%)

sample1.0s (29.4%)

Algorithm

1×

intervals

Results

371.0ms

8000×

body

128

valid

Compiler

Compiled 422 to 373 computations (11.6% saved)

Details

analyze12.0ms (0.4%)

sample228.0ms (6.6%)

simplify130.0ms (3.8%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite170.0ms (5%)

series91.0ms (2.7%)

simplify79.0ms (2.3%)

prune131.0ms (3.8%)

localize9.0ms (0.3%)

rewrite295.0ms (8.6%)

series116.0ms (3.4%)

simplify95.0ms (2.8%)

prune216.0ms (6.3%)

localize11.0ms (0.3%)

rewrite221.0ms (6.5%)

series89.0ms (2.6%)

simplify112.0ms (3.3%)

prune182.0ms (5.3%)

regimes214.0ms (6.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (29.4%)

Profiling