Details

analyze236.0ms (7.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify167.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	134	18
1	134	18

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: 2.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
0.0b	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
6.0b	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_4795` `add-sqr-sqrt_binary64_4816`
14×	`add-cube-cbrt_binary64_4827`
9×	`times-frac_binary64_4801`
8×	`add-cbrt-cube_binary64_4828` `add-log-exp_binary64_4831`
7×	`add-exp-log_binary64_4830`
6×	`pow1_binary64_4853`
3×	`associate-/r_binary64_4741` `associate-r_binary64_4737` `associate-l_binary64_4738` `associate-/l_binary64_4742`
2×	`flip3--_binary64_4799` `associate-/r/_binary64_4743` `flip--_binary64_4770`
1×	`sum-log_binary64_4883` `unswap-sqr_binary64_4763` `div-exp_binary64_4843` `clear-num_binary64_4794` `frac-2neg_binary64_4806` `sub-neg_binary64_4788` `flip3-+_binary64_4798` `flip-+_binary64_4769` `distribute-lft-out_binary64_4748` `cbrt-undiv_binary64_4826` `div-inv_binary64_4792` `*-commutative_binary64_4728` `diff-log_binary64_4884` `cbrt-unprod_binary64_4825` `+-commutative_binary64_4727` `pow-prod-down_binary64_4863` `prod-exp_binary64_4841`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))
11.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
6.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
5.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))

series386.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))
92.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
87.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
21.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4998	1527
1	4998	1527

prune90.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	3	83

Merged error: 0b

Counts

83 → 3

Compiler

Compiled 1570 to 783 computations (50.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
0.0b	(+.f64 x (/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x)))
0.0b	(/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y)
0.0b	(/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x))

rewrite48.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_4795`
28×	`add-sqr-sqrt_binary64_4816`
18×	`times-frac_binary64_4801` `add-cube-cbrt_binary64_4827`
13×	`add-exp-log_binary64_4830` `add-cbrt-cube_binary64_4828`
8×	`associate-/r*_binary64_4741`
7×	`pow1_binary64_4853`
6×	`add-log-exp_binary64_4831`
4×	`div-exp_binary64_4843` `distribute-lft-out--_binary64_4749` `associate-/l*_binary64_4742` `difference-of-squares_binary64_4764`
3×	`cbrt-undiv_binary64_4826` `div-inv_binary64_4792` `associate-r_binary64_4737` `associate-l_binary64_4738`
2×	`clear-num_binary64_4794` `frac-2neg_binary64_4806` `distribute-lft-out_binary64_4748` `associate-/r/_binary64_4743` `cbrt-unprod_binary64_4825` `prod-exp_binary64_4841`
1×	`sum-log_binary64_4883` `unswap-sqr_binary64_4763` `inv-pow_binary64_4877` `pow-flip_binary64_4866` `flip3--_binary64_4799` `1-exp_binary64_4836` `flip3-+_binary64_4798` `flip-+_binary64_4769` `*-commutative_binary64_4728` `rec-exp_binary64_4842` `flip--_binary64_4770` `+-commutative_binary64_4727` `pow-prod-down_binary64_4863`

Counts

4 → 93

Calls

4 calls:

15.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x)))
14.0ms	(/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x))
6.0ms	(/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y)
5.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))

series312.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x))
73.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y) x)))
41.0ms	(/.f64 (*.f64 5081767996463981/4503599627370496 (exp.f64 z)) y)
20.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4914	1780
1	4914	1780

prune103.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Merged error: 0b

Counts

108 → 3

Compiler

Compiled 1896 to 1187 computations (37.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 y (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
0.3b	(/.f64 1 (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
3.3b	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
3.3b	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_4816`
36×	`*-un-lft-identity_binary64_4795` `times-frac_binary64_4801` `add-cube-cbrt_binary64_4827`
30×	`sqrt-prod_binary64_4810`
12×	`associate-/r*_binary64_4741`
10×	`add-exp-log_binary64_4830`
8×	`pow1_binary64_4853` `add-cbrt-cube_binary64_4828` `sqrt-div_binary64_4811`
6×	`associate-/l*_binary64_4742`
4×	`flip3--_binary64_4799` `add-log-exp_binary64_4831` `associate-/r/_binary64_4743` `flip--_binary64_4770`
3×	`sqrt-pow1_binary64_4812` `pow1/2_binary64_4872` `div-exp_binary64_4843` `pow-flip_binary64_4866`
2×	`clear-num_binary64_4794` `frac-2neg_binary64_4806` `cbrt-undiv_binary64_4826` `div-inv_binary64_4792` `rem-sqrt-square_binary64_4808`
1×	`inv-pow_binary64_4877` `1-exp_binary64_4836` `rec-exp_binary64_4842`

Counts

4 → 118

Calls

4 calls:

11.0ms	(/.f64 1 (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
9.0ms	(/.f64 y (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
6.0ms	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
5.0ms	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))

series716.0ms (21.7%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 y (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
191.0ms	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
175.0ms	(sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
153.0ms	(/.f64 1 (sqrt.f64 (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5024	3118

prune202.0ms (6.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	130	3	133

Merged error: 0b

Counts

133 → 3

Compiler

Compiled 4364 to 2399 computations (45% saved)

regimes62.0ms (1.9%)

Compiler: Compiled 336 to 292 computations (13.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms (0%)

sample639.0ms (19.4%)

Algorithm

1×

intervals

Results

339.0ms

8000×

body

128

valid

Compiler

Compiled 86 to 75 computations (12.8% saved)

Details

analyze236.0ms (7.1%)

sample22.0ms (0.7%)

simplify167.0ms (5%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

rewrite38.0ms (1.2%)

series386.0ms (11.7%)

simplify68.0ms (2%)

prune90.0ms (2.7%)

localize9.0ms (0.3%)

rewrite48.0ms (1.4%)

series312.0ms (9.4%)

simplify73.0ms (2.2%)

prune103.0ms (3.1%)

localize13.0ms (0.4%)

rewrite45.0ms (1.4%)

series716.0ms (21.7%)

simplify61.0ms (1.9%)

prune202.0ms (6.1%)

regimes62.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample639.0ms (19.4%)

Profiling