Details

analyze392.0ms (3.2%)

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)

sample42.0ms (0.3%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	34×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify12.0ms (0.1%)

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

prune5.0ms (0%)

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)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series22.0ms (0.2%)

Counts

1 → 25

Calls

1 calls:

22.0ms

(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:

1.0ms

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

simplify112.0ms (0.9%)

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

prune23.0ms (0.2%)

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

0.1b

Counts

16 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	29.9b	(.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))))
	40.4b	(.f64 1/2 (cbrt.f64 (.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))))

Compiler

Compiled 298 to 126 computations (57.7% saved)

localize17.0ms (0.1%)

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)))
✓	0.6b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series598.0ms (4.8%)

Counts

3 → 75

Calls

3 calls:

403.0ms

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

145.0ms

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

49.0ms

(*.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)))

rewrite39.0ms (0.3%)

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:

15.0ms

(*.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)))

9.0ms

(*.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))

simplify206.0ms (1.7%)

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

prune387.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	342	6	348
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	1.4b	(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	48.9b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	2.5b	(.f64 1/2 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	37.7b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (.f64 (cbrt.f64 y) (pow.f64 z 1/6))))
	29.9b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	2.2b	(.f64 1/2 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (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 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	27.8b	(.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 13425 to 5320 computations (60.4% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
	0.6b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

series3.2s (25.4%)

Counts

1 → 25

Calls

1 calls:

3.2s	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

4.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

simplify165.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

494×	`distribute-rgt-in_binary64`
452×	`associate-l_binary64`
363×	`associate-r_binary64`
351×	`fma-def_binary64`
349×	`log-prod_binary64`

Counts

57 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1069
1	193	980
2	537	929
3	2377	692
4	4661	692
5	4951	692
6	4996	692
7	4888	692

prune144.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	123	6	129

Error

0.0b

Counts

129 → 6

Alt Table

Status	Error	Program
	48.9b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	36.6b	(*.f64 1/2 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y)))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	29.9b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
▶	2.2b	(.f64 1/2 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (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 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	27.8b	(.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 3172 to 1786 computations (43.7% saved)

localize24.0ms (0.2%)

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 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (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)))))
	0.6b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

series2.3s (18.2%)

Counts

3 → 75

Calls

3 calls:

1.6s

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

531.0ms

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

168.0ms

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

rewrite84.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`pow1_binary64`
63×	`cbrt-prod_binary64`
51×	`pow-prod-up_binary64`
51×	`pow1/3_binary64`
35×	`pow-sqr_binary64`

Counts

3 → 148

Calls

3 calls:

27.0ms

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

14.0ms

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

3.0ms

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

simplify304.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

378×	`associate-r_binary64`
344×	`unswap-sqr_binary64`
314×	`associate-l_binary64`
250×	`*-commutative_binary64`
223×	`fma-neg_binary64`

Counts

223 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	7203
1	1184	6350
2	3984	6194
3	5157	6194

prune1.8s (14.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1121	0	1121
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	1121	6	1127

Error

0.0b

Counts

1127 → 6

Alt Table

Status	Error	Program
	48.9b	(.f64 1/2 (.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	36.6b	(*.f64 1/2 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y)))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	29.9b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	2.2b	(.f64 1/2 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (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 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	27.8b	(.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 85112 to 23424 computations (72.5% saved)

regimes962.0ms (7.8%)

Accuracy

Total 0.1b remaining (45.1%)

Threshold costs 0.1b (45.1%)

Counts

53 → 1

Compiler

Compiled 10833 to 4961 computations (54.2% saved)

simplify4.0ms (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

end1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample1.7s (13.5%)

Algorithm

1×

intervals

Results

803.0ms	8000×	body	128	valid
110.0ms	1079×	body	128	nan
38.0ms	379×	body	128	invalid

Compiler

Compiled 168 to 83 computations (50.6% saved)

Details

analyze392.0ms (3.2%)

sample42.0ms (0.3%)

simplify12.0ms (0.1%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series22.0ms (0.2%)

rewrite1.0ms (0%)

simplify112.0ms (0.9%)

prune23.0ms (0.2%)

localize17.0ms (0.1%)

series598.0ms (4.8%)

rewrite39.0ms (0.3%)

simplify206.0ms (1.7%)

prune387.0ms (3.1%)

localize15.0ms (0.1%)

series3.2s (25.4%)

rewrite10.0ms (0.1%)

simplify165.0ms (1.3%)

prune144.0ms (1.2%)

localize24.0ms (0.2%)

series2.3s (18.2%)

rewrite84.0ms (0.7%)

simplify304.0ms (2.4%)

prune1.8s (14.1%)

regimes962.0ms (7.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (13.5%)

Profiling