Details

analyze13.0ms (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)

sample219.0ms (6.7%)

Algorithm

1×

intervals

Results

210.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify129.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

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)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-/l*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 58

Calls

2 calls:

12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series44.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
13.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4955	1117
1	4955	1117

prune75.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Compiler

Compiled 1174 to 946 computations (19.4% 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 (+.f64 1 x)))))
0.0b	(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
0.0b	(/.f64 1 (+.f64 1 x))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `associate-l_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

3 → 92

Calls

3 calls:

18.0ms	(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
6.0ms	(/.f64 1 (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))))

series29.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
9.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))))
8.0ms	(/.f64 1 (+.f64 1 x))

simplify65.0ms (2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5276	1324

prune105.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	101	3	104

Error

Counts

104 → 3

Compiler

Compiled 1807 to 1506 computations (16.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite211.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Rules

676×	`sqrt-prod_binary64`
596×	`*-un-lft-identity_binary64`
532×	`add-sqr-sqrt_binary64`
515×	`times-frac_binary64`
206×	`add-cube-cbrt_binary64`
149×	`swap-sqr_binary64`
92×	`difference-of-squares_binary64`
80×	`distribute-lft-out_binary64`
69×	`associate-r_binary64` `associate-l_binary64`
68×	`distribute-lft-out--_binary64`
25×	`unswap-sqr_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`sqrt-div_binary64`
13×	`pow1_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/l*_binary64`
7×	`associate-/r*_binary64`
5×	`flip3-+_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 470

Calls

4 calls:

101.0ms	(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (-.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 x))

series64.0ms (2%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (-.f64 1 x))
14.0ms	(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
14.0ms	(sqrt.f64 (-.f64 1 x))

simplify181.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

482 → 482

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4983	13471
1	4983	13471

prune1.2s (35.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	482	0	482
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	482	3	485

Error

Counts

485 → 3

Compiler

Compiled 14262 to 11765 computations (17.5% saved)

regimes85.0ms (2.6%)

Accuracy

Total 0.0b remaining (78%)

Threshold costs 0.0b (78%)

Compiler

Compiled 852 to 749 computations (12.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms (0%)

sample713.0ms (21.8%)

Algorithm

1×

intervals

Results

391.0ms

8000×

body

128

valid

Compiler

Compiled 179 to 159 computations (11.2% saved)

Details

analyze13.0ms (0.4%)

sample219.0ms (6.7%)

simplify129.0ms (3.9%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

rewrite18.0ms (0.6%)

series44.0ms (1.3%)

simplify77.0ms (2.4%)

prune75.0ms (2.3%)

localize9.0ms (0.3%)

rewrite32.0ms (1%)

series29.0ms (0.9%)

simplify65.0ms (2%)

prune105.0ms (3.2%)

localize12.0ms (0.4%)

rewrite211.0ms (6.5%)

series64.0ms (2%)

simplify181.0ms (5.5%)

prune1.2s (35.8%)

regimes85.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample713.0ms (21.8%)

Profiling