Details

analyze12.0ms (0.4%)

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)

sample229.0ms (8.7%)

Algorithm

1×

intervals

Results

221.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify132.0ms (5%)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite38.0ms (1.4%)

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:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series58.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
23.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify70.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6106	2062

prune122.0ms (4.6%)

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

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 2018 to 1628 computations (19.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`*-un-lft-identity_binary64`
150×	`sqrt-prod_binary64`
128×	`add-sqr-sqrt_binary64`
121×	`times-frac_binary64`
72×	`cbrt-prod_binary64`
66×	`unpow-prod-down_binary64` `cube-prod_binary64`
65×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`
30×	`distribute-lft-out_binary64`
20×	`distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
7×	`pow1_binary64`
5×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `sqr-pow_binary64` `cube-div_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 218

Calls

4 calls:

15.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
14.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
8.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)))

series91.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
22.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
22.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
14.0ms	(atan.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)))

simplify94.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4965	5531
1	4965	5531

prune310.0ms (11.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	230	2	232

Merged error: 0b

Counts

232 → 2

Compiler

Compiled 4935 to 4080 computations (17.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64`
99×	`cbrt-prod_binary64`
90×	`sqrt-prod_binary64`
76×	`add-sqr-sqrt_binary64`
72×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
18×	`distribute-lft-out_binary64`
12×	`distribute-lft-out--_binary64`
6×	`associate-/r/_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `flip3-+_binary64` `pow1/3_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

4 → 133

Calls

4 calls:

12.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
9.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
9.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
1.0ms	(atan.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series87.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
24.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
23.0ms	(cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
15.0ms	(atan.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

simplify94.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5000	3713

prune362.0ms (13.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	2	147

Merged error: 0b

Counts

147 → 2

Compiler

Compiled 5730 to 4656 computations (18.7% saved)

regimes102.0ms (3.9%)

Compiler: Compiled 892 to 789 computations (11.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample674.0ms (25.7%)

Algorithm

1×

intervals

Results

381.0ms

8000×

body

128

valid

Compiler

Compiled 143 to 128 computations (10.5% saved)

Details

analyze12.0ms (0.4%)

sample229.0ms (8.7%)

simplify132.0ms (5%)

prune4.0ms (0.2%)

localize9.0ms (0.3%)

rewrite38.0ms (1.4%)

series58.0ms (2.2%)

simplify70.0ms (2.7%)

prune122.0ms (4.6%)

localize10.0ms (0.4%)

rewrite63.0ms (2.4%)

series91.0ms (3.4%)

simplify94.0ms (3.6%)

prune310.0ms (11.8%)

localize11.0ms (0.4%)

rewrite51.0ms (1.9%)

series87.0ms (3.3%)

simplify94.0ms (3.6%)

prune362.0ms (13.8%)

regimes102.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample674.0ms (25.7%)

Profiling