Details

analyze255.0ms (6.3%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
46.8%	44.5%	8.7%	10
51.5%	39%	9.5%	11
57.3%	32.6%	10.1%	12
63.8%	21.6%	14.7%	13
66.2%	18.7%	15.1%	14

Compiler

Compiled 6 to 6 computations (0% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 11 to 14 computations (-27.3% saved)

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

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 10 to 10 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (+.f64 x y) z)
0.0b	(*.f64 (+.f64 x y) z)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
3×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

1 → 21

Calls

2 calls:

8.0ms	(*.f64 (+.f64 x y) z)
0.0ms	(*.f64 (+.f64 x y) z)

series104.0ms (2.6%)

Counts

1 → 15

Calls

1 calls:

104.0ms

(*.f64 (+.f64 x y) z)

Compiler

Compiled 132 to 126 computations (4.5% saved)

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5403	295

prune28.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Error

0.0b

Counts

37 → 4

Compiler

Compiled 315 to 87 computations (72.4% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (.f64 (+.f64 x y) z))) (cbrt.f64 (*.f64 (+.f64 x y) z)))
0.0b	(*.f64 (+.f64 x y) z)
0.0b	(*.f64 (+.f64 x y) z)
0.0b	(*.f64 (+.f64 x y) z)
0.6b	(.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))
3.0b	(cbrt.f64 (*.f64 (+.f64 x y) z))
3.0b	(cbrt.f64 (*.f64 (+.f64 x y) z))
3.0b	(cbrt.f64 (*.f64 (+.f64 x y) z))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*l/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

8 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))
5.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))
5.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))
4.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))
0.0ms	(*.f64 (+.f64 x y) z)

series1.1s (27.2%)

Counts

4 → 66

Calls

4 calls:

314.0ms	(.f64 (cbrt.f64 (.f64 (+.f64 x y) z)) (cbrt.f64 (*.f64 (+.f64 x y) z)))
265.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))
259.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))
255.0ms	(cbrt.f64 (*.f64 (+.f64 x y) z))

Compiler

Compiled 3753 to 2739 computations (27% saved)

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5022	2934

prune129.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Error

0.0b

Counts

142 → 4

Compiler

Compiled 3738 to 1025 computations (72.6% saved)

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 x y))))
0.1b	(*.f64 z (sqrt.f64 (+.f64 x y)))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))
0.1b	(*.f64 z (sqrt.f64 (+.f64 x y)))
0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 x y))))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`sqrt-div_binary64`
17×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
13×	`pow1_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-r/_binary64` `associate-l*_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

8 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 x y))))
7.0ms	(*.f64 z (sqrt.f64 (+.f64 x y)))
3.0ms	(sqrt.f64 (+.f64 x y))
3.0ms	(sqrt.f64 (+.f64 x y))
0.0ms	(sqrt.f64 (+.f64 x y))

series246.0ms (6.1%)

Counts

4 → 42

Calls

4 calls:

89.0ms	(*.f64 z (sqrt.f64 (+.f64 x y)))
86.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 x y))))
36.0ms	(sqrt.f64 (+.f64 x y))
33.0ms	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 910 to 750 computations (17.6% saved)

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5014	1365

prune74.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	129	4	133

Error

Counts

133 → 4

Compiler

Compiled 1750 to 368 computations (79% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (*.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y)))) (sqrt.f64 (cbrt.f64 (+.f64 x y)))))
0.2b	(.f64 (.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y)))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
0.1b	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
0.0b	(sqrt.f64 (+.f64 x y))
0.2b	(.f64 (.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y)))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
0.3b	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y))))
0.5b	(cbrt.f64 (+.f64 x y))
0.5b	(cbrt.f64 (+.f64 x y))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `pow1/3_binary64` `sqrt-div_binary64` `-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 73

Calls

8 calls:

10.0ms	(.f64 (.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y)))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
4.0ms	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y))))
3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
0.0ms	(sqrt.f64 (+.f64 x y))

series478.0ms (11.9%)

Counts

4 → 38

Calls

4 calls:

216.0ms	(.f64 (.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y)))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
88.0ms	(cbrt.f64 (+.f64 x y))
87.0ms	(cbrt.f64 (+.f64 x y))
87.0ms	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 x y))))

Compiler

Compiled 1796 to 1378 computations (23.3% saved)

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4911	1628
1	4911	1628

prune83.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	111	4	115

Error

Counts

115 → 4

Compiler

Compiled 2441 to 476 computations (80.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	148
1	45	148

regimes101.0ms (2.5%)

Compiler: Compiled 517 to 411 computations (20.5% saved)

bsearch0.0ms (0%)

regimes141.0ms (3.5%)

Compiler: Compiled 33 to 78 computations (-136.4% saved)

bsearch45.0ms (1.1%)

Steps

Iters	Range		Point
9	8.286090602471028e-70	1.9676291505141447e-63	1.942478763694612e-63
6	2.0244998783638552e-167	3.02784007329356e-166	2.076462546695796e-167
4	3.0556177385812956e-180	5.389020933597463e-180	5.291094144828729e-180
9	-7.731551708709526e+18	-88591017432.01973	-90361842115.60765

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.7%)

Compiler: Compiled 24 to 66 computations (-175% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.7%)

Accuracy

Total 0.0b remaining (57%)

Threshold costs 0.0b (57%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 41 to 34 computations (17.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	49
1	46	49

end0.0ms (0%)

sample597.0ms (14.9%)

Algorithm

1×

intervals

Results

170.0ms	8000×	body	128	valid
16.0ms	632×	body	128	invalid

Compiler

Compiled 139 to 120 computations (13.7% saved)

Pareto

0.4874872656423336

Details

analyze255.0ms (6.3%)

sample18.0ms (0.4%)

simplify104.0ms (2.6%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite11.0ms (0.3%)

series104.0ms (2.6%)

simplify63.0ms (1.6%)

prune28.0ms (0.7%)

localize9.0ms (0.2%)

rewrite29.0ms (0.7%)

series1.1s (27.2%)

simplify73.0ms (1.8%)

prune129.0ms (3.2%)

localize7.0ms (0.2%)

rewrite33.0ms (0.8%)

series246.0ms (6.1%)

simplify91.0ms (2.3%)

prune74.0ms (1.8%)

localize11.0ms (0.3%)

rewrite27.0ms (0.7%)

series478.0ms (11.9%)

simplify90.0ms (2.3%)

prune83.0ms (2.1%)

simplify4.0ms (0.1%)

regimes101.0ms (2.5%)

bsearch0.0ms (0%)

regimes141.0ms (3.5%)

bsearch45.0ms (1.1%)

regimes30.0ms (0.7%)

bsearch0.0ms (0%)

regimes26.0ms (0.7%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample597.0ms (14.9%)

Profiling