Details

analyze2.1s (8.8%)

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
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.6s (6.9%)

Results

1.3s	8256×	body	128	valid
169.0ms	204×	body	8192	exit
39.0ms	215×	body	128	invalid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify77.0ms (0.3%)

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

prune4.0ms (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

21.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.2b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 80 to 41 computations (48.8% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 b y) y)
✓	0.0b	(*.f64 z (-.f64 t a))
✓	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	20.6b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series267.0ms (1.1%)

Counts

4 → 204

Calls

4 calls:

231.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
20.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))
8.0ms	(fma.f64 z (-.f64 b y) y)
7.0ms	(*.f64 z (-.f64 t a))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 99

Calls

4 calls:

13.0ms	(*.f64 z (-.f64 t a))
2.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
0.0ms	(fma.f64 z (-.f64 b y) y)
0.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))

simplify161.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

911×	`associate-/l*_binary64`
492×	`fma-def_binary64`
260×	`+-commutative_binary64`
206×	`associate-+r+_binary64`
153×	`*-commutative_binary64`

Counts

303 → 243

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	773	10057
1	2327	9294
2	5266	9294

prune322.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	233	10	243
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	10	244

Error

0.2b

Counts

244 → 10

Alt Table

Status	Error	Program
	40.9b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))))
▶	21.3b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))
	43.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 z (-.f64 t a))) 3)) (fma.f64 z (-.f64 b y) y))
	34.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.2b	(/.f64 x (-.f64 1 z))
	21.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	21.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	26.3b	(-.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)))))
	28.7b	(-.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))))
	33.3b	(-.f64 (+.f64 (/.f64 (.f64 y x) (.f64 (-.f64 b y) z)) (+.f64 (/.f64 (.f64 a y) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y))))

Compiler

Compiled 11889 to 4439 computations (62.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	1.4b	(-.f64 (+.f64 y (.f64 z b)) (.f64 y z))
✓	20.6b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))

series252.0ms (1.1%)

Counts

2 → 99

Calls

2 calls:

244.0ms	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))
8.0ms	(-.f64 (+.f64 y (.f64 z b)) (.f64 y z))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 53

Calls

2 calls:

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

simplify134.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
686×	`associate-/l*_binary64`
543×	`fma-def_binary64`
262×	`+-commutative_binary64`
207×	`associate-+r+_binary64`

Counts

152 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	700	8903
1	2262	8010
2	5699	8010

prune313.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	270	10	280

Error

0.2b

Counts

280 → 10

Alt Table

Status	Error	Program
	40.9b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))))
✓	21.3b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))
	43.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 z (-.f64 t a))) 3)) (fma.f64 z (-.f64 b y) y))
	34.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.2b	(/.f64 x (-.f64 1 z))
▶	21.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	21.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	26.3b	(-.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)))))
	28.7b	(-.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))))
	33.3b	(-.f64 (+.f64 (/.f64 (.f64 y x) (.f64 (-.f64 b y) z)) (+.f64 (/.f64 (.f64 a y) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y))))

Compiler

Compiled 13176 to 4534 computations (65.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	0.9b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
✓	20.1b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series284.0ms (1.2%)

Counts

2 → 108

Calls

2 calls:

238.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
45.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite14.0ms (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 → 71

Calls

2 calls:

6.0ms	(.f64 (fma.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))

simplify157.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

788×	`associate-/l*_binary64`
519×	`fma-def_binary64`
318×	`+-commutative_binary64`
239×	`associate-+r+_binary64`
177×	`sub-neg_binary64`

Counts

179 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	812	10485
1	2614	9766
2	5311	9766

prune377.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	323	10	333

Error

0.2b

Counts

333 → 10

Alt Table

Status	Error	Program
	40.9b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))))
✓	21.3b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))
	43.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 z (-.f64 t a))) 3)) (fma.f64 z (-.f64 b y) y))
	34.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.2b	(/.f64 x (-.f64 1 z))
✓	21.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
▶	21.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	26.3b	(-.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)))))
	28.7b	(-.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))))
	33.3b	(-.f64 (+.f64 (/.f64 (.f64 y x) (.f64 (-.f64 b y) z)) (+.f64 (/.f64 (.f64 a y) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y))))

Compiler

Compiled 15553 to 6337 computations (59.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	20.5b	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

series671.0ms (2.8%)

Counts

2 → 144

Calls

2 calls:

454.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))
216.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
2.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

simplify241.0ms (1%)

Algorithm

1×	egg-herbie

Rules

656×	`+-commutative_binary64`
547×	`associate-+r+_binary64`
293×	`associate-/l*_binary64`
280×	`*-commutative_binary64`
202×	`associate-/r*_binary64`

Counts

251 → 304

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1525	24218
1	5092	24218

prune604.0ms (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	390	1	391
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	391	10	401

Error

0.2b

Counts

401 → 10

Alt Table

Status	Error	Program
	40.9b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) (sqrt.f64 (fma.f64 z (-.f64 b y) y))))
✓	21.3b	(/.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (-.f64 (+.f64 y (.f64 z b)) (*.f64 y z)))
	26.3b	(-.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)))))
	40.9b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) 1)) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) (fma.f64 x y (.f64 z (-.f64 t a))))))
	34.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.2b	(/.f64 x (-.f64 1 z))
✓	21.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	21.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	28.7b	(-.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))))
	33.3b	(-.f64 (+.f64 (/.f64 (.f64 y x) (.f64 (-.f64 b y) z)) (+.f64 (/.f64 (.f64 a y) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 t (-.f64 b y)))) (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 (-.f64 b y) 2) z)) (/.f64 a (-.f64 b y))))

Compiler

Compiled 29095 to 12068 computations (58.5% saved)

regimes15.7s (66.3%)

Accuracy

Total 6.2b remaining (97.1%)

Threshold costs 0b (0%)

Counts

406 → 5

Compiler

Compiled 107940 to 56991 computations (47.2% saved)

bsearch19.0ms (0.1%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	289
1	76	289
2	92	289
3	102	289
4	107	289
5	106	289

end244.0ms (1%)

Compiler: Compiled 743 to 301 computations (59.5% saved)

Details

analyze2.1s (8.8%)

sample1.6s (6.9%)

simplify77.0ms (0.3%)

prune4.0ms (0%)

localize11.0ms (0%)

series267.0ms (1.1%)

rewrite22.0ms (0.1%)

simplify161.0ms (0.7%)

prune322.0ms (1.4%)

localize14.0ms (0.1%)

series252.0ms (1.1%)

rewrite14.0ms (0.1%)

simplify134.0ms (0.6%)

prune313.0ms (1.3%)

localize12.0ms (0.1%)

series284.0ms (1.2%)

rewrite14.0ms (0.1%)

simplify157.0ms (0.7%)

prune377.0ms (1.6%)

localize12.0ms (0.1%)

series671.0ms (2.8%)

rewrite20.0ms (0.1%)

simplify241.0ms (1%)

prune604.0ms (2.6%)

regimes15.7s (66.3%)

bsearch19.0ms (0.1%)

simplify10.0ms (0%)

end244.0ms (1%)

Profiling