Details

analyze238.0ms (5.4%)

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)

sample1.1s (25.9%)

Results

943.0ms	8256×	body	128	valid
161.0ms	1488×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify7.0ms (0.2%)

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

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 66 to 47 computations (28.8% 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)

series14.0ms (0.3%)

Counts

1 → 25

Calls

1 calls:

14.0ms

(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 (2.1%)

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

prune13.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	13	4	17

Error

0.1b

Counts

17 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 1/2 (.f64 1 (fma.f64 y (sqrt.f64 z) x)))
	29.6b	(.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))))
	39.4b	(.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 312 to 137 computations (56.1% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

prune12.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Error

0.1b

Counts

19 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 1/2 (.f64 1 (fma.f64 y (sqrt.f64 z) x)))
	29.6b	(.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))))
	39.4b	(.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 330 to 158 computations (52.1% saved)

localize9.0ms (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))

series386.0ms (8.8%)

Counts

3 → 75

Calls

3 calls:

292.0ms

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

79.0ms

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

14.0ms

(*.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)))

rewrite20.0ms (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:

9.0ms

(*.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))

simplify104.0ms (2.4%)

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

prune266.0ms (6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	340	8	348
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	341	11	352

Error

0.0b

Counts

352 → 11

Alt Table

Status	Error	Program
	2.5b	(.f64 1/2 (.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	29.6b	(.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))))
	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)))))
	1.8b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.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))))
▶	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 (.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))))))
	1.8b	(.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 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
	1.8b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (.f64 (*.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))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	30.1b	(.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)))
✓	0.1b	(.f64 1/2 (.f64 1 (fma.f64 y (sqrt.f64 z) x)))
	29.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	39.4b	(.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 13707 to 5410 computations (60.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))
✓	0.5b	(cbrt.f64 (.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))))

series107.0ms (2.4%)

Counts

1 → 25

Calls

1 calls:

107.0ms

(cbrt.f64 (*.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))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

5.0ms

(cbrt.f64 (*.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))))

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
642×	`times-frac_binary64`
484×	`associate-/l*_binary64`
385×	`associate-/r*_binary64`
204×	`cancel-sign-sub-inv_binary64`

Counts

37 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1493
1	461	1461
2	1504	1348
3	4937	1346
4	5251	1346

prune450.0ms (10.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	555	5	560
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	559	12	571

Error

0.0b

Counts

571 → 12

Alt Table

Status	Error	Program
	30.1b	(.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)))
	1.6b	(.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 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)))))
	1.8b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.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))))) (cbrt.f64 (cbrt.f64 (.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)))))) (cbrt.f64 (cbrt.f64 (.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))))))))
	29.6b	(.f64 1/2 (.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	33.6b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (.f64 (cbrt.f64 y) (pow.f64 z 1/6))) (cbrt.f64 (.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))))))
	3.2b	(.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 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
	1.8b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (.f64 (*.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))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	29.6b	(.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))))
	1.8b	(.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.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))))
✓	0.1b	(.f64 1/2 (.f64 1 (fma.f64 y (sqrt.f64 z) x)))
	32.6b	(.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 (.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))))))
	39.4b	(.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 30970 to 10322 computations (66.7% saved)

regimes1.2s (27.8%)

Accuracy

Total 0.1b remaining (45%)

Threshold costs 0.1b (45%)

Counts

150 → 1

Compiler

Compiled 33961 to 15494 computations (54.4% 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

end167.0ms (3.8%)

Compiler: Compiled 460 to 173 computations (62.4% saved)

Details

analyze238.0ms (5.4%)

sample1.1s (25.9%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series14.0ms (0.3%)

rewrite1.0ms (0%)

simplify91.0ms (2.1%)

prune13.0ms (0.3%)

localize8.0ms (0.2%)

prune12.0ms (0.3%)

localize9.0ms (0.2%)

series386.0ms (8.8%)

rewrite20.0ms (0.4%)

simplify104.0ms (2.4%)

prune266.0ms (6%)

localize12.0ms (0.3%)

series107.0ms (2.4%)

rewrite6.0ms (0.1%)

simplify116.0ms (2.7%)

prune450.0ms (10.2%)

regimes1.2s (27.8%)

simplify2.0ms (0%)

end167.0ms (3.8%)

Profiling