Details

analyze52.0ms (1.4%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify347.0ms (9.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (251.0ms)

Iter	Nodes	Cost
0	3112	16
1	3112	16

prune2.0ms (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 18 computations (18.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 x y) 2)
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
7.4b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_8603`
28×	`times-frac_binary64_8609`
27×	`add-sqr-sqrt_binary64_8625`
22×	`add-cube-cbrt_binary64_8638`
18×	`cancel-sign-sub-inv_binary64_8569`
10×	`add-exp-log_binary64_8641` `add-cbrt-cube_binary64_8639`
7×	`distribute-lft-out_binary64_8554` `associate-/r*_binary64_8547`
5×	`add-log-exp_binary64_8642`
4×	`associate-/l*_binary64_8548` `associate-/r/_binary64_8549`
3×	`div-exp_binary64_8654` `cbrt-undiv_binary64_8637` `div-inv_binary64_8600` `pow1_binary64_8664`
2×	`difference-of-squares_binary64_8572` `flip3-+_binary64_8606` `flip-+_binary64_8577` `clear-num_binary64_8602` `frac-2neg_binary64_8614`
1×	`flip3--_binary64_8607` `cbrt-unprod_binary64_8636` `distribute-lft-out--_binary64_8555` `diff-log_binary64_8695` `prod-exp_binary64_8652` `flip--_binary64_8578` `sub-neg_binary64_8596`

Counts

3 → 86

Calls

3 calls:

16.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
7.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
4.0ms	(/.f64 (*.f64 x y) 2)

series242.0ms (6.4%)

Counts

3 → 47

Calls

3 calls:

94.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
93.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
55.0ms	(/.f64 (*.f64 x y) 2)

Compiler

Compiled 937 to 809 computations (13.7% saved)

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4955	2472
1	4955	2472

prune128.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

Counts

134 → 5

Compiler

Compiled 2240 to 1297 computations (42.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
0.0b	(/.f64 (*.f64 y x) 2)
0.1b	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
7.4b	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)

rewrite71.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64_8609`
160×	`*-un-lft-identity_binary64_8603`
119×	`add-sqr-sqrt_binary64_8625`
105×	`add-cube-cbrt_binary64_8638`
53×	`cancel-sign-sub-inv_binary64_8569`
25×	`distribute-lft-out_binary64_8554`
22×	`add-exp-log_binary64_8641` `associate-/r*_binary64_8547`
16×	`add-cbrt-cube_binary64_8639`
12×	`div-inv_binary64_8600`
10×	`div-exp_binary64_8654`
8×	`associate-/l*_binary64_8548`
6×	`add-log-exp_binary64_8642` `cbrt-undiv_binary64_8637`
5×	`difference-of-squares_binary64_8572` `pow1_binary64_8664`
3×	`clear-num_binary64_8602` `frac-2neg_binary64_8614`
2×	`distribute-lft-out--_binary64_8555` `associate-/l/_binary64_8550` `1-exp_binary64_8647` `rec-exp_binary64_8653` `associate-/r/_binary64_8549`
1×	`flip3-+_binary64_8606` `flip3--_binary64_8607` `cbrt-unprod_binary64_8636` `flip-+_binary64_8577` `diff-log_binary64_8695` `inv-pow_binary64_8688` `prod-exp_binary64_8652` `flip--_binary64_8578` `sub-neg_binary64_8596` `pow-flip_binary64_8677`

Counts

4 → 213

Calls

4 calls:

24.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
9.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
8.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
4.0ms	(/.f64 (*.f64 y x) 2)

series357.0ms (9.5%)

Counts

4 → 59

Calls

4 calls:

107.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
99.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
94.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
56.0ms	(/.f64 (*.f64 y x) 2)

Compiler

Compiled 1135 to 995 computations (12.3% saved)

simplify103.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5041	5842

prune280.0ms (7.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	271	1	272
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	274	3	277

Error

Counts

277 → 3

Compiler

Compiled 5117 to 3082 computations (39.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2))))
0.0b	(+.f64 (/.f64 1 y) (*.f64 x 1/2))
0.1b	(/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2)))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_8625`
22×	`*-un-lft-identity_binary64_8603`
20×	`times-frac_binary64_8609`
18×	`add-cube-cbrt_binary64_8638`
15×	`cancel-sign-sub-inv_binary64_8569`
7×	`add-log-exp_binary64_8642` `add-exp-log_binary64_8641`
5×	`add-cbrt-cube_binary64_8639`
4×	`pow1_binary64_8664` `associate-/r/_binary64_8549`
3×	`difference-of-squares_binary64_8572` `flip3-+_binary64_8606` `associate-/l_binary64_8548` `flip-+_binary64_8577` `associate-/r_binary64_8547` `div-inv_binary64_8600`
2×	`div-exp_binary64_8654` `distribute-lft-out--_binary64_8555`
1×	`flip3--_binary64_8607` `clear-num_binary64_8602` `diff-log_binary64_8695` `inv-pow_binary64_8688` `cbrt-undiv_binary64_8637` `1-exp_binary64_8647` `frac-2neg_binary64_8614` `flip--_binary64_8578` `rec-exp_binary64_8653` `sub-neg_binary64_8596` `sum-log_binary64_8694` `pow-flip_binary64_8677` `+-commutative_binary64_8533`

Counts

3 → 75

Calls

3 calls:

13.0ms	(-.f64 x (/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2))))
10.0ms	(/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2)))
7.0ms	(+.f64 (/.f64 1 y) (*.f64 x 1/2))

series230.0ms (6.1%)

Counts

3 → 53

Calls

3 calls:

81.0ms	(/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2)))
81.0ms	(-.f64 x (/.f64 1 (+.f64 (/.f64 1 y) (*.f64 x 1/2))))
68.0ms	(+.f64 (/.f64 1 y) (*.f64 x 1/2))

Compiler

Compiled 979 to 863 computations (11.8% saved)

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4889	2327
1	4889	2327

prune111.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Compiler

Compiled 2023 to 1397 computations (30.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))))
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))
1.9b	(log.f64 (exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))))
7.4b	(/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))

rewrite65.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_8603`
55×	`add-sqr-sqrt_binary64_8625`
54×	`cancel-sign-sub-inv_binary64_8569`
51×	`times-frac_binary64_8609`
40×	`add-cube-cbrt_binary64_8638`
38×	`exp-sum_binary64_8649`
22×	`log-prod_binary64_8689`
13×	`distribute-lft-out_binary64_8554`
12×	`exp-prod_binary64_8655`
9×	`add-log-exp_binary64_8642`
8×	`associate-/r/_binary64_8549`
7×	`log-pow_binary64_8692`
6×	`difference-of-squares_binary64_8572` `add-exp-log_binary64_8641` `add-cbrt-cube_binary64_8639`
5×	`pow1_binary64_8664`
4×	`flip3-+_binary64_8606` `flip-+_binary64_8577` `associate-/r*_binary64_8547` `div-inv_binary64_8600`
3×	`associate-/l*_binary64_8548` `distribute-lft-out--_binary64_8555` `sub-neg_binary64_8596`
2×	`rem-exp-log_binary64_8643` `diff-log_binary64_8695` `exp-diff_binary64_8651`
1×	`div-exp_binary64_8654` `flip3--_binary64_8607` `rem-log-exp_binary64_8644` `clear-num_binary64_8602` `cbrt-undiv_binary64_8637` `frac-2neg_binary64_8614` `log-div_binary64_8690` `flip--_binary64_8578`

Counts

4 → 138

Calls

4 calls:

18.0ms	(log.f64 (exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))))
15.0ms	(exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))))
13.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))
7.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))

series329.0ms (8.8%)

Counts

4 → 37

Calls

4 calls:

137.0ms	(log.f64 (exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))))
104.0ms	(exp.f64 (-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))))
53.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2))))
35.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 y x) 2)))

Compiler

Compiled 1010 to 828 computations (18% saved)

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5006	3674

prune170.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	175	3	178

Error

Counts

178 → 3

Compiler

Compiled 3221 to 1907 computations (40.8% saved)

regimes112.0ms (3%)

Accuracy

Total 0.0b remaining (96.5%)

Threshold costs 0.0b (96.5%)

Compiler

Compiled 986 to 794 computations (19.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms (0%)

sample794.0ms (21.1%)

Algorithm

1×

intervals

Results

269.0ms

8000×

body

128

valid

Compiler

Compiled 343 to 277 computations (19.2% saved)

Details

analyze52.0ms (1.4%)

sample15.0ms (0.4%)

simplify347.0ms (9.3%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite34.0ms (0.9%)

series242.0ms (6.4%)

simplify73.0ms (2%)

prune128.0ms (3.4%)

localize8.0ms (0.2%)

rewrite71.0ms (1.9%)

series357.0ms (9.5%)

simplify103.0ms (2.7%)

prune280.0ms (7.5%)

localize7.0ms (0.2%)

rewrite35.0ms (0.9%)

series230.0ms (6.1%)

simplify84.0ms (2.2%)

prune111.0ms (2.9%)

localize9.0ms (0.2%)

rewrite65.0ms (1.7%)

series329.0ms (8.8%)

simplify86.0ms (2.3%)

prune170.0ms (4.5%)

regimes112.0ms (3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample794.0ms (21.1%)

Profiling