Details

analyze13.0ms (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)

sample236.0ms (5.4%)

Algorithm

1×

intervals

Results

224.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify128.0ms (2.9%)

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 (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite175.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

18.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
12.0ms	(/.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)

series94.0ms (2.2%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

35.0ms	(/.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)

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	6419	2047

prune137.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	3	118

Error

0.0b

Counts

118 → 3

Compiler

Compiled 2027 to 1637 computations (19.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
0.1b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))

rewrite456.0ms (10.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

187×	`*-un-lft-identity_binary64`
125×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
66×	`cbrt-prod_binary64`
62×	`add-cube-cbrt_binary64`
60×	`unpow-prod-down_binary64` `cube-prod_binary64`
42×	`difference-of-squares_binary64`
31×	`distribute-lft-out_binary64`
21×	`distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `associate-/r*_binary64`
3×	`pow-unpow_binary64`
2×	`cube-div_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `div-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `cbrt-undiv_binary64` `associate-/l/_binary64`
1×	`pow1/3_binary64` `cbrt-div_binary64` `rem-cbrt-cube_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64`

Counts

4 → 214

Calls

4 calls:

14.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
11.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))

Compiler

Compiled 5434 to 4582 computations (15.7% saved)

series117.0ms (2.7%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

30.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
25.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
24.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
17.0ms	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))

Compiler

Compiled 777 to 736 computations (5.3% saved)

simplify97.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5413	4527

prune335.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	241	3	244

Error

0.0b

Counts

244 → 3

Compiler

Compiled 4708 to 3898 computations (17.2% saved)

localize9.0ms (0.2%)

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)))

rewrite241.0ms (5.6%)

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

Compiler

Compiled 3038 to 2537 computations (16.5% saved)

series95.0ms (2.2%)

Error

Counts

4 → 21

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
19.0ms	(sqrt.f64 (+.f64 1 x))
19.0ms	(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)

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5646	3065

prune195.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	157	4	161

Error

Counts

161 → 4

Compiler

Compiled 2975 to 2466 computations (17.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x))))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x)))

rewrite113.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64` `times-frac_binary64`
20×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
7×	`associate-/r*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out_binary64`
4×	`pow1_binary64` `sqrt-div_binary64`
3×	`add-log-exp_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64` `flip3--_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

3 → 71

Calls

3 calls:

8.0ms	(/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))
3.0ms	(atan.f64 (/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 1646 to 1406 computations (14.6% saved)

series71.0ms (1.6%)

Error

Counts

3 → 12

Calls

3 calls:

28.0ms	(/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x)))
20.0ms	(atan.f64 (/.f64 (-.f64 1 (*.f64 x 1/2)) (sqrt.f64 (+.f64 1 x))))
15.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 409 to 370 computations (9.5% saved)

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5228	1586

prune98.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	83	4	87

Error

Counts

87 → 4

Compiler

Compiled 1616 to 1377 computations (14.8% saved)

regimes255.0ms (5.9%)

Accuracy

Total 0.0b remaining (99.1%)

Threshold costs 0.0b (99.1%)

Compiler

Compiled 2643 to 2372 computations (10.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	32
1	42	32

end0.0ms (0%)

sample1.2s (27.2%)

Algorithm

1×

intervals

Results

379.0ms

8000×

body

128

valid

Compiler

Compiled 501 to 447 computations (10.8% saved)

Details

analyze13.0ms (0.3%)

sample236.0ms (5.4%)

simplify128.0ms (2.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite175.0ms (4%)

series94.0ms (2.2%)

simplify81.0ms (1.9%)

prune137.0ms (3.2%)

localize10.0ms (0.2%)

rewrite456.0ms (10.5%)

series117.0ms (2.7%)

simplify97.0ms (2.2%)

prune335.0ms (7.7%)

localize9.0ms (0.2%)

rewrite241.0ms (5.6%)

series95.0ms (2.2%)

simplify115.0ms (2.7%)

prune195.0ms (4.5%)

localize9.0ms (0.2%)

rewrite113.0ms (2.6%)

series71.0ms (1.6%)

simplify61.0ms (1.4%)

prune98.0ms (2.3%)

regimes255.0ms (5.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (27.2%)

Profiling