Details

analyze1.7s (18.6%)

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 (16.4%)

Results

1.4s	8256×	body	128	valid
42.0ms	306×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify14.0ms (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

8.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.5b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	14.1b	(/.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 b (/.f64 y t) a)
✓	2.8b	(fma.f64 y (/.f64 z t) x)
✓	8.1b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series251.0ms (2.7%)

Counts

3 → 168

Calls

3 calls:

224.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
14.0ms	(fma.f64 b (/.f64 y t) a)
13.0ms	(fma.f64 y (/.f64 z t) x)

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)

simplify131.0ms (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

prune192.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Error

0.0b

Counts

133 → 9

Alt Table

Status	Error	Program
	11.6b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	44.6b	(-.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)))))
	11.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	46.1b	(/.f64 z b)
	12.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
▶	11.3b	(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))))
	12.5b	(+.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)))))
	44.6b	(-.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)))))
	36.7b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (/.f64 z t) x) 3)) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 8100 to 3758 computations (53.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.0b	(fma.f64 b (/.f64 y t) a)
✓	2.1b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	3.1b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	7.5b	(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))))

series583.0ms (6.4%)

Counts

3 → 180

Calls

3 calls:

373.0ms

(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))))

122.0ms

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

87.0ms

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

rewrite12.0ms (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:

3.0ms

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

3.0ms

(/.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))))

simplify212.0ms (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

prune279.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	231	3	234
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	234	9	243

Error

0.0b

Counts

243 → 9

Alt Table

Status	Error	Program
	36.7b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (/.f64 z t) x) 3)) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.0b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	32.5b	(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))))
✓	11.3b	(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))))
	12.5b	(+.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)))))
	44.6b	(-.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)))))
▶	11.6b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	11.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	31.8b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))

Compiler

Compiled 13384 to 6008 computations (55.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	2.0b	(fma.f64 b (/.f64 y t) a)
	2.8b	(fma.f64 y (/.f64 z t) x)
✓	7.8b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series323.0ms (3.5%)

Counts

2 → 120

Calls

2 calls:

233.0ms	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
89.0ms	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite21.0ms (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:

8.0ms	(*.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)))

simplify164.0ms (1.8%)

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

prune279.0ms (3.1%)

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
	36.7b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (/.f64 z t) x) 3)) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.0b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	32.5b	(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))))
✓	11.3b	(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))))
	12.5b	(+.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)))))
	44.6b	(-.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)))))
✓	11.6b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
▶	11.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	31.8b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))

Compiler

Compiled 11294 to 5261 computations (53.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	2.0b	(fma.f64 b (/.f64 y t) a)
	2.8b	(fma.f64 y (/.f64 z t) x)
✓	7.9b	(/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x))

series386.0ms (4.2%)

Counts

2 → 144

Calls

2 calls:

217.0ms	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
168.0ms	(/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 125

Calls

2 calls:

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

simplify227.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

770×	`associate-/l*_binary64`
617×	`associate-/r*_binary64`
339×	`fma-def_binary64`
216×	`+-commutative_binary64`
166×	`sub-neg_binary64`

Counts

269 → 246

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	639	18072
1	2084	16988
2	5272	16988

prune347.0ms (3.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	277	9	286

Error

0.0b

Counts

286 → 9

Alt Table

Status	Error	Program
	36.7b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (/.f64 z t) x) 3)) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.0b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	32.5b	(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))))
✓	11.3b	(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))))
	12.5b	(+.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)))))
	44.6b	(-.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)))))
✓	11.6b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	11.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	31.8b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))

Compiler

Compiled 15415 to 6819 computations (55.8% saved)

regimes2.2s (24.6%)

Accuracy

Total 6.0b remaining (95.9%)

Threshold costs 0b (0%)

Counts

127 → 4

Compiler

Compiled 26239 to 16145 computations (38.5% saved)

bsearch5.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	189
1	47	189
2	46	189

end160.0ms (1.8%)

Compiler: Compiled 526 to 254 computations (51.7% saved)

Details

analyze1.7s (18.6%)

sample1.5s (16.4%)

simplify14.0ms (0.2%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series251.0ms (2.7%)

rewrite8.0ms (0.1%)

simplify131.0ms (1.4%)

prune192.0ms (2.1%)

localize14.0ms (0.2%)

series583.0ms (6.4%)

rewrite12.0ms (0.1%)

simplify212.0ms (2.3%)

prune279.0ms (3.1%)

localize11.0ms (0.1%)

series323.0ms (3.5%)

rewrite21.0ms (0.2%)

simplify164.0ms (1.8%)

prune279.0ms (3.1%)

localize12.0ms (0.1%)

series386.0ms (4.2%)

rewrite30.0ms (0.3%)

simplify227.0ms (2.5%)

prune347.0ms (3.8%)

regimes2.2s (24.6%)

bsearch5.0ms (0.1%)

simplify4.0ms (0%)

end160.0ms (1.8%)

Profiling