Details

analyze1.8s (19.3%)

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
3.9%	95.8%	0.3%	11
7.4%	92.3%	0.3%	12
8.8%	90.9%	0.3%	13
10.2%	89.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.6s (17.1%)

Results

1.5s	8256×	body	128	valid
46.0ms	288×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

prune4.0ms (0%)

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

11.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.1b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	15.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 y (/.f64 z t) x)
✓	3.3b	(fma.f64 b (/.f64 y t) a)
✓	11.3b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series277.0ms (3%)

Counts

3 → 168

Calls

3 calls:

247.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
15.0ms	(fma.f64 y (/.f64 z t) x)
14.0ms	(fma.f64 b (/.f64 y t) a)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 55

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
0.0ms	(fma.f64 y (/.f64 z t) x)
0.0ms	(fma.f64 b (/.f64 y t) a)

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
527×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
231×	`fma-def_binary64`
204×	`associate-l_binary64`

Counts

223 → 131

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	430	9216
1	1356	8684
2	4993	8684

prune218.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

0.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	36.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (sqrt.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	40.6b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	46.5b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	15.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (fma.f64 y (/.f64 z t) x) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
▶	14.5b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	33.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 y t) a) 3))))
	43.3b	(/.f64 z b)
	32.9b	(-.f64 (fma.f64 (/.f64 y (+.f64 1 a)) (/.f64 z t) (/.f64 x (+.f64 1 a))) (/.f64 (.f64 y (.f64 x b)) (*.f64 t (pow.f64 (+.f64 1 a) 2))))
	15.2b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 8110 to 3782 computations (53.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	4.3b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	7.7b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series568.0ms (6.2%)

Counts

3 → 180

Calls

3 calls:

344.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

135.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

88.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
8×	`associate-/r*_binary64`

Counts

3 → 80

Calls

3 calls:

4.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

4.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

0.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

simplify219.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/l*_binary64`
534×	`associate-/r*_binary64`
290×	`fma-def_binary64`
175×	`+-commutative_binary64`
162×	`associate-*l/_binary64`

Counts

260 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	560	16227
1	1790	15272
2	5036	15272

prune322.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	231	3	234
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	235	9	244

Error

0.0b

Counts

244 → 9

Alt Table

Status	Error	Program
	46.5b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	15.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (fma.f64 y (/.f64 z t) x) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	33.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 y t) a) 3))))
▶	13.7b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	40.6b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	15.2b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.2b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	37.6b	(fma.f64 (*.f64 (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 13420 to 6034 computations (55% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	4.3b	(/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a)))
✓	4.4b	(/.f64 (*.f64 y b) t)
✓	7.7b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series448.0ms (4.9%)

Counts

3 → 120

Calls

3 calls:

338.0ms	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
93.0ms	(/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a)))
16.0ms	(/.f64 (*.f64 y b) t)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a)))
3.0ms	(/.f64 (*.f64 y b) t)
0.0ms	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

simplify166.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-/l*_binary64`
557×	`associate-/r*_binary64`
247×	`fma-def_binary64`
163×	`associate-*l/_binary64`
151×	`+-commutative_binary64`

Counts

192 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	525	12044
1	1677	11171
2	4990	11171

prune248.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	205	9	214

Error

0.0b

Counts

214 → 9

Alt Table

Status	Error	Program
	46.5b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	15.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (fma.f64 y (/.f64 z t) x) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	33.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 y t) a) 3))))
✓	13.7b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	40.6b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
▶	15.2b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.2b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	37.6b	(fma.f64 (*.f64 (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 11650 to 5246 computations (55% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	2.0b	(fma.f64 y (/.f64 z t) x)
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	10.9b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series346.0ms (3.8%)

Counts

2 → 120

Calls

2 calls:

255.0ms	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
90.0ms	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 82

Calls

2 calls:

10.0ms	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
4.0ms	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))

simplify169.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

647×	`associate-/l*_binary64`
533×	`associate-/r*_binary64`
268×	`fma-def_binary64`
266×	`associate-l_binary64`
167×	`+-commutative_binary64`

Counts

202 → 190

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	507	12315
1	1667	11509
2	5002	11509

prune252.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	221	9	230

Error

0.0b

Counts

230 → 9

Alt Table

Status	Error	Program
	46.5b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	15.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (fma.f64 y (/.f64 z t) x) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	33.7b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 b (/.f64 y t) a) 3))))
✓	13.7b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	40.6b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
✓	15.2b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.2b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	37.6b	(fma.f64 (*.f64 (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (sqrt.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 11094 to 5151 computations (53.6% saved)

regimes2.1s (23.1%)

Accuracy

Total 7.9b remaining (93.1%)

Threshold costs 0b (0%)

Counts

142 → 4

Compiler

Compiled 32966 to 19126 computations (42% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	200
1	63	200
2	67	200
3	69	200
4	70	200
5	69	200

end175.0ms (1.9%)

Compiler: Compiled 543 to 273 computations (49.7% saved)

Details

analyze1.8s (19.3%)

sample1.6s (17.1%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series277.0ms (3%)

rewrite8.0ms (0.1%)

simplify136.0ms (1.5%)

prune218.0ms (2.4%)

localize13.0ms (0.1%)

series568.0ms (6.2%)

rewrite13.0ms (0.1%)

simplify219.0ms (2.4%)

prune322.0ms (3.5%)

localize16.0ms (0.2%)

series448.0ms (4.9%)

rewrite17.0ms (0.2%)

simplify166.0ms (1.8%)

prune248.0ms (2.7%)

localize12.0ms (0.1%)

series346.0ms (3.8%)

rewrite20.0ms (0.2%)

simplify169.0ms (1.9%)

prune252.0ms (2.8%)

regimes2.1s (23.1%)

bsearch7.0ms (0.1%)

simplify13.0ms (0.1%)

end175.0ms (1.9%)

Profiling