Details

analyze1.9s (23.9%)

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)

sample1.4s (18%)

Results

1.3s	8256×	body	128	valid
53.0ms	302×	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

14.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.3b	(/.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 b (/.f64 y t) a))
✓	2.2b	(fma.f64 y (/.f64 z t) x)
✓	2.2b	(fma.f64 b (/.f64 y t) a)
✓	14.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series281.0ms (3.6%)

Counts

4 → 216

Calls

4 calls:

232.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
19.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
16.0ms	(fma.f64 b (/.f64 y t) a)
13.0ms	(fma.f64 y (/.f64 z t) x)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 73

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
3.0ms	(fma.f64 b (/.f64 y t) a)
2.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
0.0ms	(fma.f64 y (/.f64 z t) x)

simplify131.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

289 → 158

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	9932
1	1379	9371
2	5036	9371

prune203.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	150	8	158
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	151	9	160

Error

0.0b

Counts

160 → 9

Alt Table

Status	Error	Program
	17.0b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.1b	(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))))
▶	15.9b	(+.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)))))
	42.1b	(-.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)))))
	42.7b	(/.f64 z b)
	35.8b	(/.f64 (fma.f64 y (/.f64 z t) x) (fma.f64 b (/.f64 y t) 1))
	38.7b	(*.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)))))
	38.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))

Compiler

Compiled 8557 to 3864 computations (54.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	4.5b	(/.f64 (*.f64 y b) t)
✓	4.9b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	11.5b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series312.0ms (4%)

Counts

4 → 152

Calls

4 calls:

148.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
127.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
24.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
12.0ms	(/.f64 (*.f64 y b) t)

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

16.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
10.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
7.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
3.0ms	(/.f64 (*.f64 y b) t)

simplify186.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
522×	`associate-/r*_binary64`
472×	`fma-def_binary64`
298×	`associate-l_binary64`
156×	`associate-*l/_binary64`

Counts

263 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	10630
1	1368	9571
2	4935	9243
3	5254	9243

prune267.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	266	3	269
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	270	8	278

Error

0.0b

Counts

278 → 8

Alt Table

Status	Error	Program
▶	12.0b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	16.4b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
	17.0b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.1b	(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))))
	42.1b	(-.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)))))
	27.0b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))

Compiler

Compiled 11770 to 4491 computations (61.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y b (fma.f64 a t t))
	3.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	4.5b	(/.f64 (*.f64 y b) t)
✓	11.5b	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series145.0ms (1.9%)

Counts

2 → 108

Calls

2 calls:

132.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
13.0ms	(fma.f64 y b (fma.f64 a t t))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
0.0ms	(fma.f64 y b (fma.f64 a t t))

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
480×	`cancel-sign-sub-inv_binary64`
335×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
211×	`fma-neg_binary64`

Counts

141 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4826
1	717	4480
2	3716	4438
3	5080	4438

prune231.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	223	8	231

Error

0.0b

Counts

231 → 8

Alt Table

Status	Error	Program
	17.0b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	35.8b	(+.f64 (.f64 (/.f64 y (sqrt.f64 (fma.f64 y b (fma.f64 a t t)))) (/.f64 z (sqrt.f64 (fma.f64 y b (fma.f64 a t t))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	16.1b	(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))))
	42.1b	(-.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)))))
	27.0b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	12.4b	(+.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
▶	11.6b	(+.f64 (.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 9293 to 3207 computations (65.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	4.5b	(/.f64 (*.f64 y b) t)
✓	6.3b	(*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))
✓	6.6b	(/.f64 z (fma.f64 y b (fma.f64 t a t)))

series249.0ms (3.2%)

Counts

2 → 120

Calls

2 calls:

135.0ms	(*.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t))))
113.0ms	(/.f64 z (fma.f64 y b (fma.f64 t a t)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 63

Calls

2 calls:

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

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

793×	`times-frac_binary64`
559×	`associate-/l*_binary64`
408×	`associate-/r*_binary64`
265×	`associate-r_binary64`
247×	`associate-l_binary64`

Counts

183 → 162

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	378	8731
1	1134	8284
2	5096	8284

prune279.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	276	8	284

Error

0.0b

Counts

284 → 8

Alt Table

Status	Error	Program
	17.0b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.1b	(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))))
	42.1b	(-.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)))))
	22.9b	(+.f64 (.f64 y (cbrt.f64 (pow.f64 (/.f64 z (fma.f64 y b (fma.f64 t a t))) 3))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	27.0b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	12.4b	(+.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
✓	11.6b	(+.f64 (.f64 y (/.f64 z (fma.f64 y b (fma.f64 t a t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 12341 to 4396 computations (64.4% saved)

regimes1.5s (19.5%)

Accuracy

Total 8.5b remaining (97%)

Threshold costs 0b (0%)

Counts

95 → 6

Compiler

Compiled 20375 to 12394 computations (39.2% saved)

bsearch136.0ms (1.8%)

Steps

Iters	Range		Point
10	2.0756428264463745e+40	4.2375145854686703e+52	2.0973695853553908e+40
3	8419019497009275.0	10118103572842720.0	9975149583244896.0
10	2.0354630285299795e-178	1.3416488485809222e-166	1.8963796502357436e-175
7	-1.3538072358799165e-195	-4.969645639740773e-197	-5.019015735760609e-197
10	-5.179684449286218e-35	-2.6942275238312313e-45	-5.099390865643201e-35

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

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	50	195
1	60	195
2	59	195

end191.0ms (2.5%)

Compiler: Compiled 504 to 256 computations (49.2% saved)

Details

analyze1.9s (23.9%)

sample1.4s (18%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series281.0ms (3.6%)

rewrite13.0ms (0.2%)

simplify131.0ms (1.7%)

prune203.0ms (2.6%)

localize12.0ms (0.2%)

series312.0ms (4%)

rewrite43.0ms (0.6%)

simplify186.0ms (2.4%)

prune267.0ms (3.5%)

localize14.0ms (0.2%)

series145.0ms (1.9%)

rewrite5.0ms (0.1%)

simplify109.0ms (1.4%)

prune231.0ms (3%)

localize16.0ms (0.2%)

series249.0ms (3.2%)

rewrite11.0ms (0.1%)

simplify126.0ms (1.6%)

prune279.0ms (3.6%)

regimes1.5s (19.5%)

bsearch136.0ms (1.8%)

simplify4.0ms (0.1%)

end191.0ms (2.5%)

Profiling