Details

analyze41.0ms (0.1%)

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)

sample494.0ms (1.7%)

Algorithm

1×

intervals

Results

453.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify326.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune7.0ms (0%)

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)

localize27.0ms (0.1%)

Local error

Found 2 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)))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`
6×	`distribute-lft-out_binary64`
4×	`distribute-lft-out--_binary64`
3×	`pow1_binary64`
2×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

2 → 49

Calls

2 calls:

24.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series154.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

130.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
24.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify118.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4922	1134
1	4922	1134

prune496.0ms (1.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	38	17	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	18	56

Merged error: 0b

Counts

56 → 18

Compiler

Compiled 1365 to 1135 computations (16.8% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite70.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64`
87×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
10×	`distribute-lft-out_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64`
6×	`sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`add-log-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

3 → 121

Calls

3 calls:

23.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
21.0ms	(sqrt.f64 (-.f64 1 x))
1.0ms	(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))

series85.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

41.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (-.f64 1 x))
18.0ms	(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))

simplify143.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5301	2943

prune2.3s (7.8%)

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	110	20	130
Fresh	5	11	16
Picked	0	1	1
Done	0	1	1
Total	115	33	148

Merged error: 0b

Counts

148 → 33

Compiler

Compiled 3497 to 2938 computations (16% saved)

localize28.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`sqrt-prod_binary64`
21×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
7×	`associate-/r*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `sqrt-div_binary64`
3×	`add-log-exp_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 70

Calls

3 calls:

12.0ms	(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
8.0ms	(sqrt.f64 (-.f64 1 x))
1.0ms	(atan.f64 (fabs.f64 (/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x)))))

series187.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
64.0ms	(sqrt.f64 (-.f64 1 x))
28.0ms	(atan.f64 (fabs.f64 (/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x)))))

simplify221.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5177	1770

prune1.3s (4.3%)

Pruning

40 alts after pruning (37 fresh and 3 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	3	27	30
Picked	0	1	1
Done	0	2	2
Total	72	40	112

Merged error: 0b

Counts

112 → 40

Compiler

Compiled 2705 to 2283 computations (15.6% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64`
87×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
10×	`distribute-lft-out_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64`
6×	`sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`add-log-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

3 → 121

Calls

3 calls:

21.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
8.0ms	(sqrt.f64 (-.f64 1 x))
7.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))

series83.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

42.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (-.f64 1 x))
15.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))

simplify356.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (220.0ms)

Iter	Nodes	Cost
0	5300	2953

prune2.0s (6.9%)

Pruning

49 alts after pruning (45 fresh and 4 done)

	Pruned	Kept	Total
New	115	15	130
Fresh	6	30	36
Picked	0	1	1
Done	0	3	3
Total	121	49	170

Merged error: 0b

Counts

170 → 49

Compiler

Compiled 2629 to 2166 computations (17.6% saved)

regimes5.1s (17.3%)

Compiler: Compiled 20323 to 17954 computations (11.7% saved)

bsearch3.4s (11.4%)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms (0%)

sample12.4s (42.1%)

Algorithm

1×

intervals

Results

1.1s

8000×

body

128

valid

Compiler

Compiled 3952 to 3492 computations (11.6% saved)

Pareto

Details

analyze41.0ms (0.1%)

sample494.0ms (1.7%)

simplify326.0ms (1.1%)

prune7.0ms (0%)

localize27.0ms (0.1%)

rewrite46.0ms (0.2%)

series154.0ms (0.5%)

simplify118.0ms (0.4%)

prune496.0ms (1.7%)

localize20.0ms (0.1%)

rewrite70.0ms (0.2%)

series85.0ms (0.3%)

simplify143.0ms (0.5%)

prune2.3s (7.8%)

localize28.0ms (0.1%)

rewrite35.0ms (0.1%)

series187.0ms (0.6%)

simplify221.0ms (0.7%)

prune1.3s (4.3%)

localize17.0ms (0.1%)

rewrite58.0ms (0.2%)

series83.0ms (0.3%)

simplify356.0ms (1.2%)

prune2.0s (6.9%)

regimes5.1s (17.3%)

bsearch3.4s (11.4%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample12.4s (42.1%)

Profiling