Details

analyze171.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
90.6%	9.4%	0%	7
93.7%	6.2%	0%	8
94.5%	5.5%	0%	9
95.3%	4.7%	0%	10
95.7%	4.3%	0%	11
95.8%	4.2%	0%	12
95.8%	4.2%	0%	13
95.8%	4.1%	0%	14

Compiler

Compiled 66 to 53 computations (19.7% saved)

sample1.9s (1.3%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 131 to 105 computations (19.8% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-neg_binary64`
578×	`times-frac_binary64`
564×	`cancel-sign-sub-inv_binary64`
389×	`fma-def_binary64`
380×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	93
1	91	69
2	270	69
3	825	69
4	2840	69
5	4839	69
6	5074	69

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

12.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.2b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Status

Error

Program

▶

12.2b

(-.f64 1 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

Compiler

Compiled 241 to 190 computations (21.2% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))
✓	0.5b	(*.f64 3275911/10000000 (fabs.f64 x))
✓	0.7b	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))
✓	12.1b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

series464.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

374.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
68.0ms	(+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))
20.0ms	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))
2.0ms	(*.f64 3275911/10000000 (fabs.f64 x))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`
7×	`associate-r_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
3.0ms	(*.f64 3275911/10000000 (fabs.f64 x))
3.0ms	(+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))
2.0ms	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))

simplify164.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
356×	`associate-*l/_binary64`
300×	`associate-*r/_binary64`
217×	`cancel-sign-sub-inv_binary64`
212×	`fma-neg_binary64`

Counts

116 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	6399
1	486	4719
2	1624	4340
3	4380	4340
4	4852	4340

prune1.0s (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	272	7	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	7	280

Error

12.1b

Counts

280 → 7

Alt Table

Status	Error	Program
	14.1b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (fma.f64 (.f64 (cbrt.f64 -1453152027/1000000000) (cbrt.f64 -1453152027/1000000000)) (cbrt.f64 -1453152027/1000000000) (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
▶	12.2b	(/.f64 (-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (+.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x))))))
	12.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x)))) 3)) (fma.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)) (fma.f64 (pow.f64 (exp.f64 (.f64 x x)) -2) (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)) (exp.f64 (neg.f64 (.f64 x x)))) 1))
	12.2b	(cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))))) (-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))) (-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))))
	12.8b	(log.f64 (exp.f64 (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x)))))))
	13.2b	(log.f64 (/.f64 (exp.f64 1) (exp.f64 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))))
	13.4b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (fma.f64 (sqrt.f64 1421413741/1000000000) (sqrt.f64 1421413741/1000000000) (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Compiler

Compiled 22020 to 16199 computations (26.4% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))
✓	0.5b	(*.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))
✓	0.7b	(-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000)
✓	12.1b	(-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))))

series12.9s (8.6%)

Counts

4 → 48

Calls

4 calls:

12.6s	(-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))))
262.0ms	(*.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))
72.0ms	(+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))
17.0ms	(-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000)

rewrite79.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
42×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

4 → 155

Calls

4 calls:

39.0ms	(*.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))
9.0ms	(+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))
9.0ms	(-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000)
5.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))))

simplify528.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
532×	`associate-*r/_binary64`
461×	`associate-/l*_binary64`
64×	`sqr-pow_binary64`
42×	`fma-udef_binary64`

Counts

203 → 211

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2772	37915
1	5492	37915

prune3.6s (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	453	4	457
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	458	6	464

Error

12.0b

Counts

464 → 6

Alt Table

Status	Error	Program
	14.1b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (fma.f64 (.f64 (cbrt.f64 -1453152027/1000000000) (cbrt.f64 -1453152027/1000000000)) (cbrt.f64 -1453152027/1000000000) (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
	13.4b	(/.f64 (-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))) (cbrt.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) (cbrt.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (+.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x))))))
	13.2b	(/.f64 (-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (.f64 (cbrt.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))) (cbrt.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) (.f64 (cbrt.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))))) (+.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x))))))
	13.6b	(/.f64 (-.f64 1 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) (.f64 (neg.f64 (.f64 (cbrt.f64 1453152027/1000000000) (cbrt.f64 1453152027/1000000000))) (cbrt.f64 1453152027/1000000000))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (+.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (.f64 x x))))))
	13.2b	(log.f64 (/.f64 (exp.f64 1) (exp.f64 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))))
▶	12.1b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) 3)) (+.f64 1 (.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) (+.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) 1)))) (+.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (exp.f64 (*.f64 x x))))))

Compiler

Compiled 103790 to 77068 computations (25.7% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))
✓	0.7b	(pow.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) 3)
	0.7b	(-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000)
✓	11.5b	(-.f64 1 (pow.f64 (.f64 (.f64 (/.f64 1 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (pow.f64 (exp.f64 (.f64 x x)) -2)) (.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (-.f64 (/.f64 1061405429/1000000000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)) 1453152027/1000000000) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))) (fma.f64 (fabs.f64 x) 3275911/10000000 1))))) 3))

Details

analyze171.0ms (0.1%)

sample1.9s (1.3%)

simplify59.0ms (0%)

prune6.0ms (0%)

localize20.0ms (0%)

series464.0ms (0.3%)

rewrite20.0ms (0%)

simplify164.0ms (0.1%)

prune1.0s (0.7%)

localize28.0ms (0%)

series12.9s (8.6%)

rewrite79.0ms (0.1%)

simplify528.0ms (0.4%)

prune3.6s (2.4%)

localize37.0ms (0%)

series2.1min (86%)

Profiling