Details

analyze34.0ms (1%)

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
0%	99.9%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms	240×	body	128	valid
1.0ms	9×	body	1024	valid
0.0ms	2×	body	2048	valid
0.0ms	3×	body	256	valid
0.0ms	2×	body	512	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify180.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	292	10
1	292	10

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_17300` `*-un-lft-identity_binary64_17264`
1×	`add-cbrt-cube_binary64_17297` `+-commutative_binary64_17196` `distribute-lft-out_binary64_17217` `sum-log_binary64_17352` `add-sqr-sqrt_binary64_17285` `flip-+_binary64_17238` `div-sub_binary64_17269` `add-exp-log_binary64_17299` `pow1_binary64_17322` `associate-+r-_binary64_17200` `flip3-+_binary64_17267` `add-cube-cbrt_binary64_17296`

Counts

1 → 13

Calls

1 calls:

10.0ms

(+.f64 x (/.f64 (-.f64 x y) 2))

series51.0ms (1.5%)

Counts

1 → 3

Calls

1 calls:

51.0ms

(+.f64 x (/.f64 (-.f64 x y) 2))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6330	228

prune20.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	3	17

Merged error: 0.0b

Counts

17 → 3

Compiler

Compiled 239 to 141 computations (41% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x 3/2) (.f64 y 1/2))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_17300`
1×	`add-cbrt-cube_binary64_17297` `sub-neg_binary64_17257` `flip--_binary64_17239` `add-sqr-sqrt_binary64_17285` `*-un-lft-identity_binary64_17264` `add-exp-log_binary64_17299` `pow1_binary64_17322` `flip3--_binary64_17268` `diff-log_binary64_17353` `add-cube-cbrt_binary64_17296`

Counts

1 → 11

Calls

1 calls:

4.0ms

(-.f64 (*.f64 x 3/2) (*.f64 y 1/2))

series49.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

49.0ms

(-.f64 (*.f64 x 3/2) (*.f64 y 1/2))

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5284	209

prune17.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Merged error: 0.0b

Counts

17 → 4

Compiler

Compiled 229 to 170 computations (25.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (-.f64 x y) 2))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
0.3b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))

rewrite66.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-prod_binary64_17279` `*-un-lft-identity_binary64_17264`
28×	`add-sqr-sqrt_binary64_17285`
21×	`pow1_binary64_17322`
16×	`sqrt-div_binary64_17280`
14×	`add-cube-cbrt_binary64_17296`
11×	`swap-sqr_binary64_17231`
10×	`pow1/2_binary64_17341` `sqrt-pow1_binary64_17281`
9×	`distribute-lft-out_binary64_17217` `flip-+_binary64_17238` `flip3-+_binary64_17267`
7×	`associate-l_binary64_17207` `associate-r_binary64_17206`
6×	`add-cbrt-cube_binary64_17297` `add-log-exp_binary64_17300` `add-exp-log_binary64_17299`
5×	`pow-prod-up_binary64_17331`
4×	`frac-times_binary64_17274` `unswap-sqr_binary64_17232`
3×	`pow-prod-down_binary64_17332` `pow-sqr_binary64_17237`
2×	`associate-l/_binary64_17209` `associate-r/_binary64_17208` `rem-sqrt-square_binary64_17277`
1×	`rem-square-sqrt_binary64_17276` `+-commutative_binary64_17196` `prod-exp_binary64_17310` `sum-log_binary64_17352` `cbrt-unprod_binary64_17294` `pow2_binary64_17342` `pow-plus_binary64_17324` `sqrt-unprod_binary64_17283` `*-commutative_binary64_17197` `div-sub_binary64_17269` `associate-+r-_binary64_17200`

Counts

4 → 107

Calls

4 calls:

25.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))
10.0ms	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
10.0ms	(+.f64 x (/.f64 (-.f64 x y) 2))
10.0ms	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))

series255.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
76.0ms	(sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
54.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))
42.0ms	(+.f64 x (/.f64 (-.f64 x y) 2))

simplify69.0ms (2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	2014
1	4952	2014

prune121.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	118	5	123

Merged error: 0.0b

Counts

123 → 5

Compiler

Compiled 2440 to 1372 computations (43.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))))
0.3b	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))

rewrite76.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_17264`
18×	`add-sqr-sqrt_binary64_17285`
14×	`sqrt-div_binary64_17280`
13×	`sqrt-prod_binary64_17279` `cbrt-prod_binary64_17292`
12×	`cbrt-div_binary64_17293` `add-cube-cbrt_binary64_17296`
11×	`add-cbrt-cube_binary64_17297` `add-exp-log_binary64_17299` `pow1_binary64_17322` `associate-r_binary64_17206`
10×	`associate-l_binary64_17207` `associate-*r/_binary64_17208`
9×	`flip-+_binary64_17238` `flip3-+_binary64_17267`
4×	`pow-prod-down_binary64_17332` `distribute-lft-out_binary64_17217` `prod-exp_binary64_17310` `cbrt-unprod_binary64_17294` `add-log-exp_binary64_17300` `frac-times_binary64_17274`
3×	`unswap-sqr_binary64_17232`
2×	`pow1/3_binary64_17343` `associate-l/_binary64_17209` `-commutative_binary64_17197`

Counts

4 → 87

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))))
19.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))

series1.4s (39.4%)

Counts

4 → 12

Calls

4 calls:

449.0ms	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2))))))
424.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))))
256.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))
252.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 x y) 2)))

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4918	3473
1	4918	3473

prune173.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Merged error: 0.0b

Counts

104 → 5

Compiler

Compiled 3765 to 2247 computations (40.3% saved)

regimes109.0ms (3.1%)

Compiler: Compiled 963 to 711 computations (26.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	10
1	36	10

end0.0ms (0%)

sample669.0ms (19.1%)

Algorithm

1×

intervals

Results

172.0ms	7410×	body	128	valid
19.0ms	218×	body	1024	valid
14.0ms	156×	body	2048	valid
8.0ms	147×	body	512	valid
3.0ms	69×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 286 to 216 computations (24.5% saved)

Details

analyze34.0ms (1%)

sample13.0ms (0.4%)

simplify180.0ms (5.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite11.0ms (0.3%)

series51.0ms (1.5%)

simplify57.0ms (1.6%)

prune20.0ms (0.6%)

localize5.0ms (0.1%)

rewrite5.0ms (0.1%)

series49.0ms (1.4%)

simplify49.0ms (1.4%)

prune17.0ms (0.5%)

localize7.0ms (0.2%)

rewrite66.0ms (1.9%)

series255.0ms (7.3%)

simplify69.0ms (2%)

prune121.0ms (3.5%)

localize12.0ms (0.3%)

rewrite76.0ms (2.2%)

series1.4s (39.4%)

simplify66.0ms (1.9%)

prune173.0ms (4.9%)

regimes109.0ms (3.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample669.0ms (19.1%)

Profiling