Details

analyze295.0ms (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
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.1s (14.8%)

Symmetry

(sort x y)

Results

997.0ms	8256×	body	128	valid
49.0ms	466×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

prune3.0ms (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

4.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.7b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	3.1b	(*.f64 y (fma.f64 z z 1))

series94.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

84.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
10.0ms	(*.f64 y (fma.f64 z z 1))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

5.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms	(*.f64 y (fma.f64 z z 1))

simplify120.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
451×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
296×	`associate-r_binary64`

Counts

134 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2203
1	330	1967
2	1107	1965
3	3956	1963
4	4482	1963
5	4806	1963
6	4938	1963

prune116.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Error

1.6b

Counts

123 → 6

Alt Table

Status	Error	Program
	4.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	4.9b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	4.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	17.2b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	5.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))

Compiler

Compiled 2322 to 1449 computations (37.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
✓	0.6b	(cbrt.f64 (/.f64 1 x))
✓	2.1b	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
✓	2.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))

series254.0ms (3.5%)

Counts

4 → 84

Calls

4 calls:

98.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
81.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
39.0ms	(cbrt.f64 (/.f64 1 x))
35.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))

rewrite72.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
205×	`add-sqr-sqrt_binary64`
190×	`cbrt-prod_binary64`
147×	`*-un-lft-identity_binary64`
135×	`add-cube-cbrt_binary64`

Counts

4 → 290

Calls

4 calls:

20.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
10.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
9.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
2.0ms	(cbrt.f64 (/.f64 1 x))

simplify224.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

539×	`unswap-sqr_binary64`
472×	`fma-def_binary64`
333×	`fma-neg_binary64`
304×	`associate-l_binary64`
295×	`cancel-sign-sub-inv_binary64`

Counts

374 → 446

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	8811
1	724	7584
2	2899	7460
3	3853	7377
4	5241	7377

prune527.0ms (7.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	494	6	500
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	496	10	506

Error

0.7b

Counts

506 → 10

Alt Table

Status	Error	Program
	4.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	17.2b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	46.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
	4.7b	(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
✓	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
▶	4.3b	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	4.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	4.9b	(/.f64 1 (.f64 y (+.f64 (.f64 (pow.f64 z 2) x) x)))
	45.9b	(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
	46.0b	(.f64 (.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 y))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 y))))

Compiler

Compiled 15556 to 11127 computations (28.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
	0.6b	(cbrt.f64 (/.f64 1 x))
	2.1b	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
✓	2.8b	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))

series117.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

89.0ms	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
28.0ms	(cbrt.f64 x)

rewrite265.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

990×	`times-frac_binary64`
633×	`add-sqr-sqrt_binary64`
500×	`cbrt-prod_binary64`
408×	`*-un-lft-identity_binary64`
388×	`add-cube-cbrt_binary64`

Counts

2 → 445

Calls

2 calls:

150.0ms	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
1.0ms	(cbrt.f64 x)

simplify355.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-*l/_binary64`
575×	`associate-*r/_binary64`
398×	`*-commutative_binary64`
327×	`associate-/l*_binary64`
310×	`associate-/r/_binary64`

Counts

493 → 799

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	423	17380
1	1307	16693
2	4003	16543
3	4950	16543

prune913.0ms (12.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	974	1	975
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	974	11	985

Error

0.7b

Counts

985 → 11

Alt Table

Status	Error	Program
▶	4.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	17.2b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	46.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
	4.7b	(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
✓	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
✓	4.3b	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	4.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	4.9b	(/.f64 1 (.f64 y (+.f64 (.f64 (pow.f64 z 2) x) x)))
	46.1b	(*.f64 (/.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (sqrt.f64 x))) (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (sqrt.f64 x))) (sqrt.f64 y)) (hypot.f64 1 z)))
	45.9b	(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
	46.0b	(.f64 (.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 y))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (sqrt.f64 y))))

Compiler

Compiled 34694 to 21089 computations (39.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	2.1b	(/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1))
✓	2.8b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))

series228.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

98.0ms	(/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1))
93.0ms	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite98.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
258×	`add-sqr-sqrt_binary64`
194×	`add-exp-log_binary64`
176×	`*-un-lft-identity_binary64`
162×	`add-cube-cbrt_binary64`

Counts

3 → 337

Calls

3 calls:

36.0ms	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
6.0ms	(/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

simplify373.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
425×	`associate-/r/_binary64`
401×	`fma-neg_binary64`
385×	`associate-*l/_binary64`
377×	`associate-*r/_binary64`

Counts

409 → 522

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	358	11682
1	957	9605
2	3038	8824
3	4513	8824
4	5111	8824

prune581.0ms (7.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	575	1	576
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	577	10	587

Error

0.7b

Counts

587 → 10

Alt Table

Status	Error	Program
✓	4.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	17.2b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	46.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
	4.7b	(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
✓	4.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
✓	4.3b	(*.f64 (/.f64 (/.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	4.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	4.9b	(/.f64 1 (.f64 y (+.f64 (.f64 (pow.f64 z 2) x) x)))
	46.1b	(.f64 (/.f64 (/.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (hypot.f64 1 z)) (.f64 (cbrt.f64 x) (sqrt.f64 y))) (/.f64 (/.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (hypot.f64 1 z)) (*.f64 (cbrt.f64 x) (sqrt.f64 y))))
	45.9b	(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))

Compiler

Compiled 17113 to 8992 computations (47.5% saved)

regimes1.2s (16.2%)

Accuracy

Total 1.4b remaining (36.3%)

Threshold costs 0b (0%)

Counts

106 → 3

Compiler

Compiled 19790 to 14258 computations (28% saved)

bsearch55.0ms (0.7%)

Steps

Iters	Range		Point
7	1.509186561328299e-31	9.742673890142287e-30	5.838039238768918e-31
10	-3.467691649491087e-301	1.0547749380001102e-302	-3.70384347346874e-310

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	106
1	41	106
2	40	106

end309.0ms (4.2%)

Compiler: Compiled 512 to 358 computations (30.1% saved)

Details

analyze295.0ms (4%)

sample1.1s (14.8%)

simplify11.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series94.0ms (1.3%)

rewrite12.0ms (0.2%)

simplify120.0ms (1.6%)

prune116.0ms (1.6%)

localize9.0ms (0.1%)

series254.0ms (3.5%)

rewrite72.0ms (1%)

simplify224.0ms (3.1%)

prune527.0ms (7.2%)

localize12.0ms (0.2%)

series117.0ms (1.6%)

rewrite265.0ms (3.6%)

simplify355.0ms (4.8%)

prune913.0ms (12.4%)

localize11.0ms (0.2%)

series228.0ms (3.1%)

rewrite98.0ms (1.3%)

simplify373.0ms (5.1%)

prune581.0ms (7.9%)

regimes1.2s (16.2%)

bsearch55.0ms (0.7%)

simplify3.0ms (0%)

end309.0ms (4.2%)

Profiling