Details

analyze2.0s (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.4s (0.9%)

Results

1.3s	8255×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

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

25.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.1b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 51 computations (46.9% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	1.2b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	23.5b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series180.0ms (0.1%)

Counts

3 → 204

Calls

3 calls:

140.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
26.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
13.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

6.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
0.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

simplify150.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11356
1	1961	11106
2	5078	11106

prune194.0ms (0.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	187	13	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	13	201

Error

3.5b

Counts

201 → 13

Alt Table

Status	Error	Program
▶	25.1b	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))
	25.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	40.8b	a
	43.7b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	32.1b	(-.f64 (+.f64 a z) b)
	48.5b	z
	52.7b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	45.5b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	41.9b	(/.f64 (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b))) (+.f64 x y))
	45.1b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	51.2b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	38.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	25.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

Compiler

Compiled 10621 to 3153 computations (70.3% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 a b))
	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	3.4b	(+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a)))
✓	23.5b	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))

series171.0ms (0.1%)

Counts

3 → 168

Calls

3 calls:

137.0ms	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))
27.0ms	(+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a)))
6.0ms	(*.f64 y (-.f64 a b))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`distribute-lft-in_binary64`

Counts

3 → 132

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))
7.0ms	(+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a)))
5.0ms	(*.f64 y (-.f64 a b))

simplify163.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

692×	`associate-/l*_binary64`
459×	`associate-/r*_binary64`
274×	`+-commutative_binary64`
232×	`fma-def_binary64`
209×	`associate-+r+_binary64`

Counts

300 → 290

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	759	11890
1	2065	11604
2	5087	11604

prune226.0ms (0.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	316	13	329

Error

3.5b

Counts

329 → 13

Alt Table

Status	Error	Program
✓	25.1b	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))
	25.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	40.8b	a
	43.7b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	32.1b	(-.f64 (+.f64 a z) b)
	48.5b	z
	52.7b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	45.5b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	41.9b	(/.f64 (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b))) (+.f64 x y))
	45.1b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	51.2b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
	38.2b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
▶	25.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

Compiler

Compiled 14111 to 3651 computations (74.1% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.2b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	23.6b	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

series1.7s (1.2%)

Counts

2 → 144

Calls

2 calls:

1.6s	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
135.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
132×	`times-frac_binary64`
68×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
48×	`distribute-lft-out_binary64`

Counts

2 → 141

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
6.0ms	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify411.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l*_binary64`
436×	`times-frac_binary64`
336×	`fma-def_binary64`
77×	`sub-neg_binary64`
46×	`sqr-pow_binary64`

Counts

285 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2784	46779
1	5617	46779

prune687.0ms (0.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	369	3	372
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	371	14	385

Error

3.5b

Counts

385 → 14

Alt Table

Status	Error	Program
	34.6b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 z (+.f64 x y) (*.f64 a (+.f64 t y)))))
✓	25.1b	(/.f64 (+.f64 (.f64 y (-.f64 a b)) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))
▶	25.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	40.8b	a
	43.7b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	32.1b	(-.f64 (+.f64 a z) b)
	52.7b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	38.2b	(/.f64 1 (/.f64 (+.f64 t x) (fma.f64 a t (*.f64 z x))))
	48.5b	(/.f64 1 (/.f64 1 z))
	45.5b	(/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))
	41.9b	(/.f64 (+.f64 (.f64 z (+.f64 x y)) (.f64 y (-.f64 a b))) (+.f64 x y))
	45.1b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	51.2b	(/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x)))
✓	25.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

Compiler

Compiled 54730 to 20830 computations (61.9% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
✓	0.5b	(cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t))))
	1.2b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
	23.5b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series2.4min (94.9%)

Calls

1 calls:

38.4s

(cbrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t))))

Details

analyze2.0s (1.4%)

sample1.4s (0.9%)

simplify93.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0%)

series180.0ms (0.1%)

rewrite11.0ms (0%)

simplify150.0ms (0.1%)

prune194.0ms (0.1%)

localize13.0ms (0%)

series171.0ms (0.1%)

rewrite34.0ms (0%)

simplify163.0ms (0.1%)

prune226.0ms (0.2%)

localize14.0ms (0%)

series1.7s (1.2%)

rewrite38.0ms (0%)

simplify411.0ms (0.3%)

prune687.0ms (0.5%)

localize16.0ms (0%)

series2.4min (94.9%)

Profiling