Details

analyze1.7s (18.8%)

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)

sample1.5s (16.9%)

Results

1.4s	8256×	body	128	valid
49.0ms	294×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify21.0ms (0.2%)

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

11.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.8b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	14.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.9b	(fma.f64 y (/.f64 z t) x)
✓	3.3b	(fma.f64 b (/.f64 y t) a)
✓	11.5b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series248.0ms (2.8%)

Counts

3 → 168

Calls

3 calls:

221.0ms	(/.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)
12.0ms	(fma.f64 b (/.f64 y t) a)

rewrite7.0ms (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)

simplify120.0ms (1.4%)

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

prune182.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Error

0.3b

Counts

133 → 11

Alt Table

Status	Error	Program
	37.7b	(*.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)))))
▶	14.3b	(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))))
	33.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (cbrt.f64 (.f64 (.f64 (fma.f64 b (/.f64 y t) a) (fma.f64 b (/.f64 y t) a)) (fma.f64 b (/.f64 y t) a)))))
	45.2b	(-.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)))))
	42.2b	(/.f64 (.f64 y z) (.f64 t (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	32.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	15.5b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	45.4b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	43.6b	(/.f64 z b)
	14.9b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.4b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))

Compiler

Compiled 8222 to 3814 computations (53.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	5.4b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	7.6b	(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))))

series489.0ms (5.5%)

Counts

3 → 180

Calls

3 calls:

288.0ms

(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))))

117.0ms

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

83.0ms

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

rewrite15.0ms (0.2%)

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:

7.0ms

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

4.0ms

(/.f64 y (+.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))))

simplify206.0ms (2.3%)

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

prune296.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	230	4	234
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	235	10	245

Error

Counts

245 → 10

Alt Table

Status	Error	Program
	16.5b	(+.f64 (/.f64 (.f64 y z) (.f64 t (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.5b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
▶	14.2b	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.7b	(*.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)))))
	37.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	45.2b	(-.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)))))
	45.4b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	40.1b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	14.9b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.4b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))

Compiler

Compiled 13502 to 6070 computations (55% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.9b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	5.2b	(*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	7.6b	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series372.0ms (4.2%)

Counts

2 → 120

Calls

2 calls:

285.0ms	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
87.0ms	(*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

10.0ms	(*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
0.0ms	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

simplify155.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/l*_binary64`
546×	`associate-/r*_binary64`
298×	`associate-l_binary64`
246×	`fma-def_binary64`
152×	`+-commutative_binary64`

Counts

173 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	490	11576
1	1617	10816
2	5061	10816

prune326.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	262	10	272

Error

Counts

272 → 10

Alt Table

Status	Error	Program
	16.5b	(+.f64 (/.f64 (.f64 y z) (.f64 t (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.5b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
✓	14.2b	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.7b	(*.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)))))
	37.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	45.2b	(-.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)))))
	45.4b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	40.1b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
▶	14.9b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.4b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))

Compiler

Compiled 14813 to 6779 computations (54.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	1.9b	(fma.f64 y (/.f64 z t) x)
	3.3b	(fma.f64 b (/.f64 y t) a)
✓	11.4b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series284.0ms (3.2%)

Counts

2 → 120

Calls

2 calls:

212.0ms	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
71.0ms	(/.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:

9.0ms	(*.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)))

simplify174.0ms (2%)

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

prune249.0ms (2.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	221	10	231

Error

Counts

231 → 10

Alt Table

Status	Error	Program
	16.5b	(+.f64 (/.f64 (.f64 y z) (.f64 t (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.5b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
✓	14.2b	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	37.7b	(*.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)))))
	37.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	45.2b	(-.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)))))
	45.4b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	40.1b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
✓	14.9b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	15.4b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))

Compiler

Compiled 11135 to 5169 computations (53.6% saved)

regimes2.2s (24.9%)

Accuracy

Total 7.7b remaining (97.9%)

Threshold costs 0b (0%)

Counts

98 → 5

Compiler

Compiled 22909 to 13516 computations (41% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	218
1	58	218
2	57	218

end236.0ms (2.7%)

Compiler: Compiled 608 to 295 computations (51.5% saved)

Details

analyze1.7s (18.8%)

sample1.5s (16.9%)

simplify21.0ms (0.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series248.0ms (2.8%)

rewrite7.0ms (0.1%)

simplify120.0ms (1.4%)

prune182.0ms (2.1%)

localize11.0ms (0.1%)

series489.0ms (5.5%)

rewrite15.0ms (0.2%)

simplify206.0ms (2.3%)

prune296.0ms (3.4%)

localize15.0ms (0.2%)

series372.0ms (4.2%)

rewrite14.0ms (0.2%)

simplify155.0ms (1.8%)

prune326.0ms (3.7%)

localize12.0ms (0.1%)

series284.0ms (3.2%)

rewrite20.0ms (0.2%)

simplify174.0ms (2%)

prune249.0ms (2.8%)

regimes2.2s (24.9%)

bsearch4.0ms (0%)

simplify4.0ms (0.1%)

end236.0ms (2.7%)

Profiling