Details

analyze12.0ms (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
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)

sample231.0ms (6.6%)

Algorithm

1×

intervals

Results

222.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify189.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	165	17
1	165	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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize17.0ms (0.5%)

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))

rewrite34.0ms (1%)

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:

12.0ms	(/.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))))

series105.0ms (3%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
36.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
22.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify73.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5073	2078

prune227.0ms (6.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Merged error: 0b

Counts

110 → 8

Compiler

Compiled 3436 to 2855 computations (16.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))))
0.0b	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x)))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
0.0b	(.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))

rewrite79.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`associate-l_binary64`
28×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
14×	`distribute-lft-out_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
6×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
5×	`sqrt-div_binary64`
4×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-/r/_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

26.0ms	(.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))
20.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x)))))
13.0ms	(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
1.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))))

series191.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x)))))
47.0ms	(.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))
41.0ms	(/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))
33.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (.f64 1 x))))))

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5472	3749

prune270.0ms (7.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	142	8	150

Merged error: 0b

Counts

150 → 8

Compiler

Compiled 4623 to 3404 computations (26.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 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))
0.0b	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))

rewrite65.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
81×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
50×	`difference-of-squares_binary64`
36×	`associate-l_binary64`
32×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
5×	`associate-/r*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

23.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
14.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
11.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
1.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))

series138.0ms (4%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
41.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
28.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
23.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))

simplify79.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5046	3335

prune212.0ms (6.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	163	8	171

Merged error: 0b

Counts

171 → 8

Compiler

Compiled 3973 to 2848 computations (28.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite70.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64`
106×	`add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
90×	`sqrt-prod_binary64`
66×	`exp-prod_binary64`
52×	`add-cube-cbrt_binary64`
34×	`log-pow_binary64` `difference-of-squares_binary64`
25×	`distribute-lft-out_binary64`
17×	`distribute-lft-out--_binary64`
8×	`associate-/r/_binary64`
6×	`pow1_binary64` `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`
2×	`associate-/l/_binary64` `rem-sqrt-square_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 179

Calls

4 calls:

15.0ms	(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
13.0ms	(exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series215.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
62.0ms	(exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
49.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
22.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5408	3305

prune266.0ms (7.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	191	8	199

Merged error: 0b

Counts

199 → 8

Compiler

Compiled 3966 to 3261 computations (17.8% saved)

regimes79.0ms (2.3%)

Compiler: Compiled 702 to 619 computations (11.8% 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%)

sample724.0ms (20.8%)

Algorithm

1×

intervals

Results

425.0ms

8000×

body

128

valid

Compiler

Compiled 149 to 133 computations (10.7% saved)

Details

analyze12.0ms (0.3%)

sample231.0ms (6.6%)

simplify189.0ms (5.4%)

prune4.0ms (0.1%)

localize17.0ms (0.5%)

rewrite34.0ms (1%)

series105.0ms (3%)

simplify73.0ms (2.1%)

prune227.0ms (6.5%)

localize15.0ms (0.4%)

rewrite79.0ms (2.3%)

series191.0ms (5.5%)

simplify83.0ms (2.4%)

prune270.0ms (7.8%)

localize10.0ms (0.3%)

rewrite65.0ms (1.9%)

series138.0ms (4%)

simplify79.0ms (2.3%)

prune212.0ms (6.1%)

localize11.0ms (0.3%)

rewrite70.0ms (2%)

series215.0ms (6.2%)

simplify83.0ms (2.4%)

prune266.0ms (7.6%)

regimes79.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample724.0ms (20.8%)

Profiling