Details

analyze1.9s (10.7%)

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
12.5%	87.2%	0.3%	7
12.5%	87.2%	0.3%	8
18.7%	81%	0.3%	9
21.8%	77.9%	0.3%	10
21.8%	77.9%	0.3%	11
21.8%	77.9%	0.3%	12
37.4%	62.3%	0.3%	13
37.4%	62.3%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample2.0s (11.6%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 71 to 44 computations (38% saved)

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
593×	`fma-def_binary64`
507×	`div-sub_binary64`
484×	`sub-neg_binary64`
470×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	21
2	50	21
3	93	21
4	157	21
5	270	21
6	423	21
7	724	21
8	1341	21
9	3898	21
10	4400	21
11	4952	21

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

21.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.8b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

Compiler

Compiled 84 to 45 computations (46.4% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 b y))
✓	0.0b	(*.f64 z (-.f64 t a))
✓	0.2b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
✓	21.7b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

series449.0ms (2.6%)

Counts

4 → 204

Calls

4 calls:

372.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
32.0ms	(*.f64 z (-.f64 b y))
30.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
14.0ms	(*.f64 z (-.f64 t a))

rewrite81.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
54×	`prod-diff_binary64`
39×	`distribute-lft-in_binary64`

Counts

4 → 173

Calls

4 calls:

22.0ms	(*.f64 z (-.f64 t a))
11.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
11.0ms	(*.f64 z (-.f64 b y))
11.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))

simplify359.0ms (2%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/r*_binary64`
602×	`fma-def_binary64`
286×	`+-commutative_binary64`
206×	`associate-+r+_binary64`
190×	`*-commutative_binary64`

Counts

377 → 329

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	900	10724
1	2568	10008
2	5761	10008

prune616.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	322	7	329
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	322	8	330

Error

0.0b

Counts

330 → 8

Alt Table

Status	Error	Program
	25.0b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
✓	21.8b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
▶	21.9b	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	25.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	43.2b	(/.f64 (/.f64 (fma.f64 z (-.f64 t a) (.f64 y x)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (+.f64 y (.f64 z (-.f64 b y)))))
	30.2b	(/.f64 (-.f64 t a) (-.f64 b y))
	22.2b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
	40.5b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 14886 to 4876 computations (67.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.2b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
✓	1.1b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
✓	20.5b	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series442.0ms (2.5%)

Counts

2 → 108

Calls

2 calls:

383.0ms	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
58.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
2.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

simplify195.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-/l*_binary64`
553×	`fma-def_binary64`
321×	`+-commutative_binary64`
239×	`associate-+r+_binary64`
182×	`sub-neg_binary64`

Counts

183 → 244

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	829	10660
1	2704	9941
2	5712	9941

prune419.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	375	0	375
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	375	8	383

Error

0.0b

Counts

383 → 8

Alt Table

Status	Error	Program
	25.0b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
✓	21.8b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
✓	21.9b	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	25.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	43.2b	(/.f64 (/.f64 (fma.f64 z (-.f64 t a) (.f64 y x)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (+.f64 y (.f64 z (-.f64 b y)))))
	30.2b	(/.f64 (-.f64 t a) (-.f64 b y))
▶	22.2b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
	40.5b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 17402 to 6590 computations (62.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 z) (-.f64 b y))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.7b	(cbrt.f64 z)
✓	21.7b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))

series749.0ms (4.3%)

Counts

4 → 132

Calls

4 calls:

412.0ms	(*.f64 (cbrt.f64 z) (-.f64 b y))
212.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
68.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
57.0ms	(cbrt.f64 z)

rewrite237.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
23×	`cbrt-prod_binary64`
18×	`prod-diff_binary64`

Counts

4 → 142

Calls

4 calls:

142.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
12.0ms	(*.f64 (cbrt.f64 z) (-.f64 b y))
8.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify319.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

803×	`associate-/l*_binary64`
566×	`fma-def_binary64`
263×	`+-commutative_binary64`
206×	`associate-+r+_binary64`
190×	`*-commutative_binary64`

Counts

274 → 291

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	830	10017
1	2500	9013
2	5563	9013

prune485.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	325	8	333

Error

0.0b

Counts

333 → 8

Alt Table

Status	Error	Program
▶	25.0b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
✓	21.8b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
✓	21.9b	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	25.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	43.2b	(/.f64 (/.f64 (fma.f64 z (-.f64 t a) (.f64 y x)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (+.f64 y (.f64 z (-.f64 b y)))))
	30.2b	(/.f64 (-.f64 t a) (-.f64 b y))
✓	22.2b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
	40.5b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 15713 to 5024 computations (68% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.9b	(/.f64 a (pow.f64 (-.f64 y b) 2))
✓	7.9b	(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))
✓	10.1b	(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
✓	11.3b	(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))

series801.0ms (4.6%)

Counts

4 → 188

Calls

4 calls:

324.0ms	(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))
221.0ms	(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
143.0ms	(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))
112.0ms	(/.f64 a (pow.f64 (-.f64 y b) 2))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
20×	`unpow-prod-down_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 a (pow.f64 (-.f64 y b) 2))
1.0ms	(fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))
1.0ms	(fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b)))
1.0ms	(fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b))))

simplify326.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

494×	`associate-+r+_binary64`
367×	`fma-neg_binary64`
312×	`associate-/l*_binary64`
305×	`associate-+l+_binary64`
284×	`times-frac_binary64`

Counts

277 → 232

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	502	10158
1	1293	9496
2	4899	9496
3	5217	9496

prune370.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	0	4	4
Picked	0	1	1
Done	1	2	3
Total	231	9	240

Error

0.0b

Counts

240 → 9

Alt Table

Status	Error	Program
✓	21.9b	(.f64 (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	25.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	40.9b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (/.f64 (+.f64 (/.f64 (.f64 y x) (-.f64 y b)) (/.f64 (.f64 y t) (pow.f64 (-.f64 y b) 2))) z))
✓	22.2b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (-.f64 b y)))))
	43.2b	(/.f64 (/.f64 (fma.f64 z (-.f64 t a) (.f64 y x)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (+.f64 y (.f64 z (-.f64 b y)))))
	38.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (neg.f64 (/.f64 (+.f64 t (/.f64 (*.f64 y x) z)) b)))
✓	25.0b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	30.2b	(/.f64 (-.f64 t a) (-.f64 b y))
	40.5b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 13580 to 4587 computations (66.2% saved)

regimes7.3s (41.4%)

Accuracy

Total 7.7b remaining (97.8%)

Threshold costs 0b (0%)

Counts

156 → 3

Compiler

Compiled 42915 to 22922 computations (46.6% saved)

bsearch43.0ms (0.2%)

Steps

Iters	Range		Point
8	1.802968710248029e+48	1.7379739630019135e+51	1.8313071631021404e+48
7	-4.870015591460113e+24	-2.804306986309133e+22	-3.9399606018418395e+22

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`*-commutative_binary64`
12×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	120
1	58	120
2	79	120
3	98	120
4	109	120
5	113	120
6	114	120
7	114	120

end210.0ms (1.2%)

Compiler: Compiled 454 to 224 computations (50.7% saved)

Details

analyze1.9s (10.7%)

sample2.0s (11.6%)

simplify137.0ms (0.8%)

prune10.0ms (0.1%)

localize29.0ms (0.2%)

series449.0ms (2.6%)

rewrite81.0ms (0.5%)

simplify359.0ms (2%)

prune616.0ms (3.5%)

localize24.0ms (0.1%)

series442.0ms (2.5%)

rewrite16.0ms (0.1%)

simplify195.0ms (1.1%)

prune419.0ms (2.4%)

localize19.0ms (0.1%)

series749.0ms (4.3%)

rewrite237.0ms (1.3%)

simplify319.0ms (1.8%)

prune485.0ms (2.8%)

localize19.0ms (0.1%)

series801.0ms (4.6%)

rewrite30.0ms (0.2%)

simplify326.0ms (1.9%)

prune370.0ms (2.1%)

regimes7.3s (41.4%)

bsearch43.0ms (0.2%)

simplify7.0ms (0%)

end210.0ms (1.2%)

Profiling