Details

analyze12.0ms (0.5%)

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)

sample218.0ms (8.9%)

Algorithm

1×

intervals

Results

210.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify129.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (0.2%)

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 (0.4%)

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))

rewrite39.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

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×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series60.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
23.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
13.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify72.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6106	2062

prune132.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Error

Counts

110 → 2

Compiler

Compiled 2002 to 1614 computations (19.4% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b

(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))

0.0b

(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))

0.0b

(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))

rewrite42.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
36×	`associate-l_binary64`
31×	`times-frac_binary64`
24×	`difference-of-squares_binary64`
18×	`add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

3 → 93

Calls

3 calls:

20.0ms

(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))

12.0ms

(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))

1.0ms

(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))

series59.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

24.0ms

(sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x)))

19.0ms

(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))

16.0ms

(atan.f64 (sqrt.f64 (*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))))

simplify69.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6109	2058

prune124.0ms (5.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	102	2	104

Error

Counts

104 → 2

Compiler

Compiled 2404 to 1714 computations (28.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite65.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64`
90×	`exp-prod_binary64`
62×	`log-pow_binary64`
51×	`add-cube-cbrt_binary64`
34×	`difference-of-squares_binary64` `sqrt-prod_binary64`
25×	`distribute-lft-out_binary64`
17×	`distribute-lft-out--_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`log-prod_binary64` `div-sub_binary64`
2×	`associate-/l/_binary64` `exp-diff_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 177

Calls

4 calls:

13.0ms	(sqrt.f64 (log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
12.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
10.0ms	(exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

series85.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
20.0ms	(exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
19.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify94.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5553	3158

prune241.0ms (9.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	189	2	191

Error

Counts

191 → 2

Compiler

Compiled 3768 to 3062 computations (18.7% saved)

regimes152.0ms (6.2%)

Accuracy

Total 0.0b remaining (93.8%)

Threshold costs 0.0b (93.8%)

Compiler

Compiled 1578 to 1375 computations (12.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	26
1	34	26

end0.0ms (0%)

sample817.0ms (33.4%)

Algorithm

1×

intervals

Results

373.0ms

8000×

body

128

valid

Compiler

Compiled 292 to 254 computations (13% saved)

Details

analyze12.0ms (0.5%)

sample218.0ms (8.9%)

simplify129.0ms (5.3%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

rewrite39.0ms (1.6%)

series60.0ms (2.4%)

simplify72.0ms (2.9%)

prune132.0ms (5.4%)

localize9.0ms (0.4%)

rewrite42.0ms (1.7%)

series59.0ms (2.4%)

simplify69.0ms (2.8%)

prune124.0ms (5.1%)

localize10.0ms (0.4%)

rewrite65.0ms (2.6%)

series85.0ms (3.5%)

simplify94.0ms (3.8%)

prune241.0ms (9.9%)

regimes152.0ms (6.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample817.0ms (33.4%)

Profiling