Details

analyze228.0ms (7%)

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 (34%)

Results

917.0ms	8256×	body	128	valid
150.0ms	1514×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	38	10
3	48	10

Stop Event

1×

saturated

Counts

1 → 2

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)

series12.0ms (0.4%)

Counts

1 → 25

Calls

1 calls:

12.0ms

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

rewrite33.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log1p-expm1-u_binary64`
499×	`expm1-log1p-u_binary64`
339×	`unpow-prod-down_binary64`
266×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	118	7
2	1378	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

33.0ms

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

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	10	148
2	11	148

Stop Event

1×

saturated

Counts

61 → 39

prune24.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

0.1b

Counts

40 → 7

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	40.3b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
	34.8b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
	29.9b	(.f64 1/2 (/.f64 (-.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 2) (*.f64 x x)) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
	40.6b	(.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 2) (-.f64 (.f64 x x) (.f64 (.f64 y (sqrt.f64 z)) x)))))
	2.2b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2) 3) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
▶	1.3b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))

Compiler

Compiled 774 to 386 computations (50.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
✓	0.5b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)

series132.0ms (4.1%)

Counts

3 → 43

Calls

3 calls:

81.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
41.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
10.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	200	28
2	2005	28

Stop Event

1×	node limit

Counts

3 → 60

Calls

3 calls:

48.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
48.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
48.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

662×	`associate-r_binary64`
661×	`fma-neg_binary64`
655×	`associate-l_binary64`
437×	`fma-def_binary64`
276×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1007
1	342	1003
2	1083	984
3	4918	984

Stop Event

1×	node limit

Counts

103 → 94

prune119.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	207	4	211
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	209	9	218

Error

0.0b

Counts

218 → 9

Alt Table

Status	Error	Program
	43.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (.f64 y (.f64 y z)))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	12.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4)))))
	40.3b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
	34.8b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
	29.9b	(.f64 1/2 (/.f64 (-.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 2) (*.f64 x x)) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
✓	1.3b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
▶	1.8b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	41.0b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))

Compiler

Compiled 5814 to 2765 computations (52.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)

series202.0ms (6.3%)

Counts

2 → 50

Calls

2 calls:

149.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)
54.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
148×	`expm1-udef_binary64`
148×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	196	20
2	2046	20

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

39.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
39.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

397×	`cancel-sign-sub-inv_binary64`
247×	`associate-r_binary64`
240×	`unswap-sqr_binary64`
201×	`associate-l_binary64`
191×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3162
1	801	3080
2	3138	2964

Stop Event

1×	node limit

Counts

97 → 127

prune175.0ms (5.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	238	10	248

Error

0.0b

Counts

248 → 10

Alt Table

Status	Error	Program
	43.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (.f64 y (.f64 y z)))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	1.9b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	34.8b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
	12.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4)))))
	40.3b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
	29.9b	(.f64 1/2 (/.f64 (-.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 2) (*.f64 x x)) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
✓	1.3b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
✓	1.8b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	41.0b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))

Compiler

Compiled 9612 to 5491 computations (42.9% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.5b	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3))
✓	0.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) 3)
	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)

series206.0ms (6.4%)

Counts

2 → 50

Calls

2 calls:

150.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) 3)
55.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3))

rewrite43.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log1p-expm1-u_binary64`
723×	`expm1-log1p-u_binary64`
148×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	226	20
2	2075	20

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

42.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3))
42.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) 3)

simplify65.0ms (2%)

Algorithm

1×	egg-herbie

Rules

397×	`cancel-sign-sub-inv_binary64`
247×	`associate-r_binary64`
240×	`unswap-sqr_binary64`
201×	`associate-l_binary64`
191×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3162
1	801	3080
2	3138	2964

Stop Event

1×	node limit

Counts

97 → 127

prune222.0ms (6.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	254	10	264

Error

0.0b

Counts

264 → 10

Alt Table

Status	Error	Program
	43.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (.f64 y (.f64 y z)))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
✓	1.9b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	34.8b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
	12.9b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4)))))
	40.3b	(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
	29.9b	(.f64 1/2 (/.f64 (-.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 2) (*.f64 x x)) (fma.f64 y (sqrt.f64 z) (neg.f64 x))))
✓	1.3b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
✓	1.8b	(.f64 1/2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	41.0b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))

Compiler

Compiled 11525 to 6950 computations (39.7% saved)

regimes242.0ms (7.5%)

Accuracy

Total 0.1b remaining (49.5%)

Threshold costs 0.1b (49.5%)

Counts

27 → 1

Compiler

Compiled 4150 to 2793 computations (32.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10

Stop Event

1×

saturated

end159.0ms (4.9%)

Compiler: Compiled 231 to 145 computations (37.2% saved)

Details

analyze228.0ms (7%)

sample1.1s (34%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series12.0ms (0.4%)

rewrite33.0ms (1%)

simplify9.0ms (0.3%)

prune24.0ms (0.8%)

localize10.0ms (0.3%)

series132.0ms (4.1%)

rewrite49.0ms (1.5%)

simplify48.0ms (1.5%)

prune119.0ms (3.7%)

localize13.0ms (0.4%)

series202.0ms (6.3%)

rewrite44.0ms (1.4%)

simplify69.0ms (2.1%)

prune175.0ms (5.4%)

localize15.0ms (0.5%)

series206.0ms (6.4%)

rewrite43.0ms (1.3%)

simplify65.0ms (2%)

prune222.0ms (6.9%)

regimes242.0ms (7.5%)

simplify3.0ms (0.1%)

end159.0ms (4.9%)

Profiling