Details

analyze1.7s (13.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.9s (14.4%)

Results

1.2s	8256×	body	128	valid
595.0ms	3979×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.6b	(.f64 (.f64 a z) b)

series44.0ms (0.3%)

Counts

3 → 144

Calls

3 calls:

27.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
9.0ms	(+.f64 x (*.f64 y z))
8.0ms	(.f64 (.f64 a z) b)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`sum-log_binary64`

Counts

3 → 55

Calls

3 calls:

6.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

644×	`distribute-rgt-in_binary64`
620×	`distribute-lft-in_binary64`
604×	`fma-def_binary64`
535×	`fma-neg_binary64`
210×	`associate-+l+_binary64`

Counts

199 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2151
1	339	1861
2	1237	1850
3	4736	1850
4	5113	1850

prune75.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

Counts

106 → 7

Alt Table

Status	Error	Program
	3.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))))
▶	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	17.9b	(fma.f64 z (fma.f64 a b y) x)
	46.3b	(/.f64 (+.f64 (pow.f64 (.f64 a (.f64 z b)) 3) (pow.f64 (fma.f64 z y (fma.f64 a t x)) 3)) (fma.f64 a (.f64 (.f64 z b) (.f64 a (.f64 z b))) (.f64 (fma.f64 z y (fma.f64 a t x)) (fma.f64 a (-.f64 t (.f64 z b)) (fma.f64 z y x)))))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	21.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (sqrt.f64 (.f64 a (.f64 z b))) (sqrt.f64 (.f64 a (*.f64 z b)))))
	3.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))

Compiler

Compiled 2386 to 532 computations (77.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series40.0ms (0.3%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
17.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 a (fma.f64 z b t) x)
0.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
732×	`associate-+r+_binary64`
701×	`fma-def_binary64`
559×	`associate-l_binary64`
480×	`associate-r_binary64`

Counts

152 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1737
1	97	1579
2	249	1579
3	1063	1579
4	5721	1579

prune57.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Error

Counts

73 → 7

Alt Table

Status	Error	Program
	3.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	17.9b	(fma.f64 z (fma.f64 a b y) x)
	46.3b	(/.f64 (+.f64 (pow.f64 (.f64 a (.f64 z b)) 3) (pow.f64 (fma.f64 z y (fma.f64 a t x)) 3)) (fma.f64 a (.f64 (.f64 z b) (.f64 a (.f64 z b))) (.f64 (fma.f64 z y (fma.f64 a t x)) (fma.f64 a (-.f64 t (.f64 z b)) (fma.f64 z y x)))))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	21.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (sqrt.f64 (.f64 a (.f64 z b))) (sqrt.f64 (.f64 a (*.f64 z b)))))
▶	3.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))

Compiler

Compiled 1266 to 334 computations (73.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
✓	5.9b	(.f64 a (.f64 z b))
✓	13.3b	(cbrt.f64 (.f64 a (.f64 z b)))

series2.2s (16.7%)

Counts

4 → 124

Calls

4 calls:

1.4s	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
723.0ms	(cbrt.f64 (.f64 a (.f64 z b)))
50.0ms	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
11.0ms	(.f64 a (.f64 z b))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`pow1/3_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`pow-prod-up_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
6.0ms	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
4.0ms	(.f64 a (.f64 z b))
2.0ms	(cbrt.f64 (.f64 a (.f64 z b)))

simplify167.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

540×	`exp-prod_binary64`
427×	`exp-diff_binary64`
393×	`fma-neg_binary64`
361×	`*-commutative_binary64`
355×	`exp-sum_binary64`

Counts

223 → 134

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	196	3303
1	429	3058
2	1055	2635
3	2674	2383
4	4449	2227
5	4869	2227
6	4323	2220
7	5087	2220

prune210.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	230	7	237

Error

Counts

237 → 7

Alt Table

Status	Error	Program
	21.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 a (.f64 z b)))) (sqrt.f64 (cbrt.f64 (.f64 a (*.f64 z b)))))))
▶	3.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	17.9b	(fma.f64 z (fma.f64 a b y) x)
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	21.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (sqrt.f64 (.f64 a (.f64 z b))) (sqrt.f64 (.f64 a (*.f64 z b)))))
✓	3.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))

Compiler

Compiled 8352 to 1440 computations (82.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))))
✓	0.5b	(.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (*.f64 a z) b))))
✓	0.6b	(cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))
	4.6b	(.f64 (.f64 a z) b)

series3.8s (28.7%)

Counts

3 → 216

Calls

3 calls:

3.1s

(*.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))))

632.0ms

(cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)))

35.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))))

rewrite108.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`
29×	`pow1_binary64`

Counts

3 → 129

Calls

3 calls:

26.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))))

16.0ms

(*.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))))

6.0ms

(cbrt.f64 (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)))

simplify487.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

345 → 274

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5189	77142

prune1.4s (10.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	532	7	539

Error

Counts

539 → 7

Alt Table

Status	Error	Program
	21.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 a (.f64 z b)))) (sqrt.f64 (cbrt.f64 (.f64 a (*.f64 z b)))))))
✓	3.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)))) (cbrt.f64 (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	17.9b	(fma.f64 z (fma.f64 a b y) x)
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	21.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (sqrt.f64 (.f64 a (.f64 z b))) (sqrt.f64 (.f64 a (*.f64 z b)))))
✓	3.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))

Compiler

Compiled 91670 to 44196 computations (51.8% saved)

regimes547.0ms (4.1%)

Accuracy

Total 0.5b remaining (98%)

Threshold costs 0.5b (98%)

Counts

57 → 3

Compiler

Compiled 9890 to 5211 computations (47.3% saved)

bsearch36.0ms (0.3%)

Steps

Iters	Range		Point
6	6.877637058708764e+123	3.088824947573861e+124	7.145324265213525e+123
3	-2.6607245361940163e+57	-1.040784229510417e+34	-9.112644010531083e+36

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	31	69
2	31	69

end189.0ms (1.4%)

Compiler: Compiled 324 to 139 computations (57.1% saved)

Details

analyze1.7s (13.2%)

sample1.9s (14.4%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series44.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify87.0ms (0.7%)

prune75.0ms (0.6%)

localize8.0ms (0.1%)

series40.0ms (0.3%)

rewrite1.0ms (0%)

simplify53.0ms (0.4%)

prune57.0ms (0.4%)

localize14.0ms (0.1%)

series2.2s (16.7%)

rewrite24.0ms (0.2%)

simplify167.0ms (1.3%)

prune210.0ms (1.6%)

localize14.0ms (0.1%)

series3.8s (28.7%)

rewrite108.0ms (0.8%)

simplify487.0ms (3.7%)

prune1.4s (10.2%)

regimes547.0ms (4.1%)

bsearch36.0ms (0.3%)

simplify6.0ms (0%)

end189.0ms (1.4%)

Profiling