Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 66 to 53 computations (19.7% saved)

sample3.6s (5.8%)

Results

3.5s

8256×

body

128

valid

Compiler

Compiled 197 to 158 computations (19.8% saved)

simplify73.0ms (0.1%)

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

prune15.0ms (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

11.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.6b	(-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (.f64 x x)))))
▶	11.6b	(-.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

11.6b

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

▶

11.6b

(-.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 335 to 262 computations (21.8% saved)

localize44.0ms (0.1%)

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))))
✓	0.4b	(*.f64 3275911/10000000 (fabs.f64 x))
✓	0.7b	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))
✓	11.5b	(-.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))))))

series850.0ms (1.4%)

Counts

4 → 36

Calls

4 calls:

664.0ms	(-.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))))))
143.0ms	(+.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))))
38.0ms	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))
4.0ms	(*.f64 3275911/10000000 (fabs.f64 x))

rewrite88.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

301×	`log1p-expm1-u_binary64`
301×	`expm1-log1p-u_binary64`
296×	`add-log-exp_binary64`
294×	`add-cbrt-cube_binary64`
294×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

84.0ms	(+.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))))
84.0ms	(*.f64 3275911/10000000 (fabs.f64 x))
84.0ms	(+.f64 -1453152027/1000000000 (.f64 (/.f64 1 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))
84.0ms	(-.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))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	131
1	640	115
2	5235	115
0	0	0
1	0	0

simplify223.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-neg_binary64`
569×	`fma-def_binary64`
412×	`times-frac_binary64`
336×	`associate-/r*_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

109 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	2208
1	125	1848
2	335	1704
3	1120	1572
4	4271	1548
5	4964	1548
6	4996	1548
7	4915	1548

prune645.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	124	5	129

Error

11.5b

Counts

129 → 5

Alt Table

Status	Error	Program
	11.6b	(-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (.f64 x x)))))
	12.7b	(-.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 (pow.f64 (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 2) (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) -1453152027/1000000000)))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
	12.2b	(log.f64 (exp.f64 (-.f64 1 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
▶	11.6b	(/.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(-.f64 (+.f64 1 (+.f64 (.f64 1453152027/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 4))) (.f64 8890523/31250000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (.f64 31853699/125000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (.f64 1061405429/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 5))) (.f64 1421413741/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 3))))))

Compiler

Compiled 9220 to 6785 computations (26.4% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
✓	0.4b	(pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)
✓	0.7b	(+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
✓	11.1b	(-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))

series2.5s (4%)

Counts

4 → 48

Calls

4 calls:

1.9s	(-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))
508.0ms	(pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)
67.0ms	(+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
17.0ms	(+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))

rewrite57.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

289×	`log1p-expm1-u_binary64`
289×	`expm1-log1p-u_binary64`
284×	`add-cbrt-cube_binary64`
282×	`add-log-exp_binary64`
280×	`add-exp-log_binary64`

Counts

4 → 76

Calls

4 calls:

54.0ms	(+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
54.0ms	(pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)
54.0ms	(+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
54.0ms	(-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	183
1	623	183
2	4955	183
0	0	0
1	0	0

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-+r+_binary64`
496×	`fma-def_binary64`
422×	`associate-+l+_binary64`
174×	`times-frac_binary64`
166×	`associate-/r*_binary64`

Counts

124 → 101

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	9208
1	1260	8340
2	5134	8340

prune1.1s (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	192	6	198

Error

10.8b

Counts

198 → 6

Alt Table

Status	Error	Program
	12.2b	(/.f64 (-.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3) (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))))))
	12.2b	(log.f64 (exp.f64 (-.f64 1 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	11.6b	(-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (.f64 x x)))))
	12.7b	(/.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 2) (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) -1453152027/1000000000) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
▶	10.8b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(-.f64 (+.f64 1 (+.f64 (.f64 1453152027/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 4))) (.f64 8890523/31250000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (.f64 31853699/125000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (.f64 1061405429/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 5))) (.f64 1421413741/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 3))))))

Compiler

Compiled 37143 to 26483 computations (28.7% saved)

localize30.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))
	0.7b	(+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
✓	11.0b	(log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))))
	11.1b	(-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))

series47.4s (76.7%)

Counts

2 → 24

Calls

2 calls:

41.3s

(log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (*.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))) 3)))))

6.2s

(expm1.f64 (-.f64 1 (pow.f64 (*.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))) 3)))

rewrite55.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

311×	`log1p-expm1-u_binary64`
311×	`expm1-log1p-u_binary64`
303×	`add-cbrt-cube_binary64`
302×	`add-log-exp_binary64`
300×	`add-exp-log_binary64`

Counts

2 → 39

Calls

2 calls:

51.0ms

(expm1.f64 (-.f64 1 (pow.f64 (*.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))) 3)))

51.0ms

(log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (*.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))) 3)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	150
1	666	150
2	5338	150
0	0	0
1	0	0

simplify626.0ms (1%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-def_binary64`
510×	`times-frac_binary64`
472×	`associate-/l*_binary64`
265×	`+-commutative_binary64`
250×	`associate-+r+_binary64`

Counts

63 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	781	43459
1	2575	38813
2	5198	38813

prune2.0s (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	155	6	161

Error

10.8b

Counts

161 → 6

Alt Table

Status	Error	Program
	11.6b	(-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (.f64 x x)))))
	13.5b	(/.f64 (log.f64 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))) 2) (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))) -1))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(/.f64 (-.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3) (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))))))
	12.7b	(/.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 2) (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) -1453152027/1000000000) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(-.f64 (+.f64 1 (+.f64 (.f64 1453152027/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 4))) (.f64 8890523/31250000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (.f64 31853699/125000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (.f64 1061405429/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 5))) (.f64 1421413741/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 3))))))
▶	10.8b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (cbrt.f64 (pow.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 3)) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))

Compiler

Compiled 80061 to 62573 computations (21.8% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))
✓	1.2b	(cbrt.f64 (pow.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 3))
	11.0b	(log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))))
	11.1b	(-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))

series19.0ms (0%)

Counts

1 → 12

Calls

1 calls:

19.0ms

(cbrt.f64 (pow.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 3))

rewrite81.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

426×	`log-prod_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
190×	`pow1/3_binary64`
168×	`pow3_binary64`

Counts

1 → 45

Calls

1 calls:

80.0ms

(cbrt.f64 (pow.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	13
1	261	11
2	2686	11
3	4993	11
4	4915	11
0	0	0
1	0	0

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`fma-def_binary64`
2×	`fma-neg_binary64`
1×	`associate-*r/_binary64`

Counts

57 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	180
1	23	156
2	28	156
3	24	156

prune1.0s (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	175	6	181

Error

10.8b

Counts

181 → 6

Alt Table

Status	Error	Program
	11.6b	(-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (.f64 x x)))))
	13.5b	(/.f64 (log.f64 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))) 2) (cbrt.f64 (exp.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)))) -1))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(/.f64 (-.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3) (pow.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x))))) 3))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (*.f64 x x)))))))
	12.7b	(/.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 2) (cbrt.f64 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) -1453152027/1000000000) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3)) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))
	12.2b	(-.f64 (+.f64 1 (+.f64 (.f64 1453152027/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 4))) (.f64 8890523/31250000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (.f64 31853699/125000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (.f64 1061405429/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 5))) (.f64 1421413741/1000000000 (/.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))) (pow.f64 (+.f64 1 (.f64 3275911/10000000 (fabs.f64 x))) 3))))))
✓	10.8b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 3))))) (+.f64 1 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (cbrt.f64 (pow.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) 3)) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))) 2) (.f64 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (neg.f64 (.f64 x x)))))))

Compiler

Compiled 35498 to 25682 computations (27.7% saved)

regimes724.0ms (1.2%)

Accuracy

Total 0.0b remaining (0.3%)

Threshold costs 0.0b (0.3%)

Counts

51 → 1

Compiler

Compiled 29716 to 21833 computations (26.5% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	228
1	67	228
2	74	228
3	79	228
4	81	228
5	80	228

end509.0ms (0.8%)

Compiler: Compiled 1151 to 843 computations (26.8% saved)

Details

analyze2.0ms (0%)

sample3.6s (5.8%)

simplify73.0ms (0.1%)

prune15.0ms (0%)

localize44.0ms (0.1%)

series850.0ms (1.4%)

rewrite88.0ms (0.1%)

simplify223.0ms (0.4%)

prune645.0ms (1%)

localize53.0ms (0.1%)

series2.5s (4%)

rewrite57.0ms (0.1%)

simplify141.0ms (0.2%)

prune1.1s (1.7%)

localize30.0ms (0%)

series47.4s (76.7%)

rewrite55.0ms (0.1%)

simplify626.0ms (1%)

prune2.0s (3.2%)

localize48.0ms (0.1%)

series19.0ms (0%)

rewrite81.0ms (0.1%)

simplify13.0ms (0%)

prune1.0s (1.6%)

regimes724.0ms (1.2%)

simplify8.0ms (0%)

end509.0ms (0.8%)

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