Details

analyze331.0ms (8.1%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (28.3%)

Results

968.0ms	8256×	body	128	valid
161.0ms	1504×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
10×	`fma-def_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	35	10
3	41	10
4	39	10

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 z) x)

series10.0ms (0.2%)

Counts

1 → 25

Calls

1 calls:

10.0ms

(fma.f64 y (sqrt.f64 z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (sqrt.f64 z) x)

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
436×	`distribute-rgt-out_binary64`
421×	`associate-l_binary64`
413×	`*-commutative_binary64`

Counts

35 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	262
1	20	247
2	43	247
3	104	247
4	281	247
5	915	247
6	1563	247
7	2177	247
8	2401	247
9	3023	247
10	3557	247
11	4430	247
12	4903	247

prune15.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Alt Table

Status	Error	Program
	31.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
▶	1.4b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	40.1b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Compiler

Compiled 278 to 126 computations (54.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.5b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series186.0ms (4.5%)

Counts

3 → 75

Calls

3 calls:

118.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

54.0ms

(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

1.0ms

(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

simplify105.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

374×	`cancel-sign-sub-inv_binary64`
265×	`associate-r_binary64`
242×	`associate-/r/_binary64`
235×	`associate-l_binary64`
225×	`unswap-sqr_binary64`

Counts

168 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	4425
1	842	4181
2	2818	3870
3	4974	3870

prune202.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	344	4	348
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	31.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
▶	1.7b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	40.1b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
✓	1.4b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	2.1b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	28.8b	(.f64 1/2 (.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))

Compiler

Compiled 13344 to 5296 computations (60.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
	0.5b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

series165.0ms (4%)

Counts

2 → 50

Calls

2 calls:

116.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
49.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

10.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

simplify106.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

770×	`associate-/l*_binary64`
352×	`cancel-sign-sub-inv_binary64`
249×	`associate-r_binary64`
242×	`associate-/r/_binary64`
205×	`associate-l_binary64`

Counts

122 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	4828
1	831	4586
2	2777	4279
3	5572	4279

prune485.0ms (11.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	632	1	633
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	632	9	641

Error

0.0b

Counts

641 → 9

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	31.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	1.7b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	40.1b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
✓	1.4b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
▶	2.1b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	49.7b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (.f64 (pow.f64 y 1/9) (pow.f64 z 1/18))))
	28.8b	(.f64 1/2 (.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))

Compiler

Compiled 38605 to 13082 computations (66.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
	0.5b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.2b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)

series316.0ms (7.7%)

Counts

2 → 50

Calls

2 calls:

300.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)
16.0ms	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite69.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
13×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`

Counts

2 → 69

Calls

2 calls:

62.0ms	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

991×	`times-frac_binary64`
485×	`fma-def_binary64`
436×	`unswap-sqr_binary64`
203×	`associate-r_binary64`
190×	`associate-l_binary64`

Counts

119 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	3483
1	601	3100
2	2081	2750
3	4984	2750
4	4948	2750

prune223.0ms (5.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	308	9	317

Error

0.0b

Counts

317 → 9

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	31.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	1.7b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	40.1b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
✓	1.4b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	2.1b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	49.7b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (.f64 (pow.f64 y 1/9) (pow.f64 z 1/18))))
	28.8b	(.f64 1/2 (.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))

Compiler

Compiled 11920 to 6012 computations (49.6% saved)

regimes319.0ms (7.8%)

Accuracy

Total 0.1b remaining (38.2%)

Threshold costs 0.1b (38.2%)

Counts

37 → 1

Compiler

Compiled 6679 to 3362 computations (49.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
2	9	10

end127.0ms (3.1%)

Compiler: Compiled 233 to 116 computations (50.2% saved)

Details

analyze331.0ms (8.1%)

sample1.2s (28.3%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify91.0ms (2.2%)

prune15.0ms (0.4%)

localize8.0ms (0.2%)

series186.0ms (4.5%)

rewrite16.0ms (0.4%)

simplify105.0ms (2.6%)

prune202.0ms (4.9%)

localize11.0ms (0.3%)

series165.0ms (4%)

rewrite17.0ms (0.4%)

simplify106.0ms (2.6%)

prune485.0ms (11.9%)

localize9.0ms (0.2%)

series316.0ms (7.7%)

rewrite69.0ms (1.7%)

simplify104.0ms (2.5%)

prune223.0ms (5.4%)

regimes319.0ms (7.8%)

simplify2.0ms (0%)

end127.0ms (3.1%)

Profiling