Details

analyze1.1s (8.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample145.0ms (1.1%)

Algorithm

1×

intervals

Results

19.0ms	39×	body	1024	valid
16.0ms	171×	body	128	valid
9.0ms	33×	body	512	valid
8.0ms	18×	body	1024	nan
5.0ms	59×	body	128	nan
4.0ms	15×	body	512	nan
2.0ms	12×	body	256	valid
2.0ms	12×	body	256	nan
0.0ms	1×	body	2048	valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
506×	`fma-neg_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	103	39
3	222	39
4	455	39
5	975	39
6	2136	39
7	4390	39
8	4971	39

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

42.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))

Compiler

Compiled 114 to 72 computations (36.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	13.2b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	20.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series2.6s (19.7%)

Counts

4 → 120

Calls

4 calls:

2.2s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
324.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
76.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
10.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
9.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
4.0ms	(*.f64 (sqrt.f64 2) t)

simplify435.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

388×	`fma-def_binary64`
343×	`associate-+r+_binary64`
286×	`associate-r_binary64`
228×	`associate-*r/_binary64`
219×	`associate-/l*_binary64`

Counts

210 → 258

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1626	31940
1	5000	31940
2	5024	31940

prune839.0ms (6.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	248	10	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	10	259

Error

5.8b

Counts

259 → 10

Alt Table

Status	Error	Program
	41.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (neg.f64 (.f64 l l))) (fma.f64 (neg.f64 l) l (*.f64 l l)))))
▶	33.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	38.7b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	62.9b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2)))) (*.f64 t (sqrt.f64 2)))
	42.3b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	47.6b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 2) x))))))
	38.2b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))

Compiler

Compiled 42331 to 31206 computations (26.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(/.f64 (*.f64 t t) x)
✓	15.0b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	28.0b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

series318.0ms (2.4%)

Counts

4 → 108

Calls

4 calls:

247.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))
30.0ms	(/.f64 (.f64 t t) (.f64 x x))
30.0ms	(/.f64 (.f64 l l) (.f64 x x))
10.0ms	(/.f64 (*.f64 t t) x)

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-cbrt-cube_binary64`
33×	`add-exp-log_binary64`
10×	`cbrt-undiv_binary64`
10×	`div-exp_binary64`
9×	`cbrt-unprod_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(/.f64 (.f64 l l) (.f64 x x))
5.0ms	(/.f64 (.f64 t t) (.f64 x x))
3.0ms	(/.f64 (*.f64 t t) x)
1.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

simplify169.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

662×	`times-frac_binary64`
501×	`fma-def_binary64`
392×	`associate-/r*_binary64`
355×	`associate-/l*_binary64`
207×	`associate-*l/_binary64`

Counts

192 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	536	9498
1	1568	7984
2	4986	7982
3	4976	7982

prune349.0ms (2.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	168	7	175
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	171	14	185

Error

0.5b

Counts

185 → 14

Alt Table

Status	Error	Program
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	62.9b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2)))) (*.f64 t (sqrt.f64 2)))
▶	33.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	47.6b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	38.2b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	38.7b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
	33.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	42.3b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	38.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 (.f64 x x) t)))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	33.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))

Compiler

Compiled 15655 to 8963 computations (42.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.9b	(/.f64 (*.f64 t t) x)
	15.0b	(/.f64 (.f64 l l) (.f64 x x))
	17.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	28.0b	(sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

series249.0ms (1.9%)

Counts

1 → 36

Calls

1 calls:

249.0ms

(sqrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (*.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (*.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
289×	`associate-/r*_binary64`
281×	`associate-r_binary64`
253×	`associate-l_binary64`
221×	`times-frac_binary64`

Counts

51 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	445	7783
1	1380	6606
2	5018	6606

prune693.0ms (5.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	350	14	364

Error

0.5b

Counts

364 → 14

Alt Table

Status	Error	Program
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	62.9b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2)))) (*.f64 t (sqrt.f64 2)))
✓	33.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	47.6b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	38.2b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	38.7b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
▶	33.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	42.3b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	38.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 (.f64 x x) t)))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	33.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))

Compiler

Compiled 42885 to 20159 computations (53% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.9b	(/.f64 (*.f64 t t) x)
	15.0b	(/.f64 (.f64 l l) (.f64 x x))
	17.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	28.9b	(cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

series481.0ms (3.6%)

Counts

1 → 36

Calls

1 calls:

479.0ms

(cbrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (*.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (*.f64 x x)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

622×	`times-frac_binary64`
560×	`associate-/r*_binary64`
550×	`fma-def_binary64`
408×	`associate-/l*_binary64`
211×	`*-commutative_binary64`

Counts

49 → 87

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	563	10702
1	1904	9742
2	5336	9742

prune821.0ms (6.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	352	0	352
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	352	14	366

Error

0.5b

Counts

366 → 14

Alt Table

Status	Error	Program
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	62.9b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2)))) (*.f64 t (sqrt.f64 2)))
✓	33.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	47.6b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	38.2b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	38.7b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	37.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t)))
✓	33.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	42.3b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	38.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 (.f64 x x) t)))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	33.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))

Compiler

Compiled 51444 to 27060 computations (47.4% saved)

regimes1.8s (13.4%)

Accuracy

Total 11.9b remaining (96.5%)

Threshold costs 0b (0%)

Counts

87 → 4

Compiler

Compiled 29442 to 18274 computations (37.9% saved)

bsearch252.0ms (1.9%)

Steps

Iters	Range	Point
8	4.306451856362919e+21	9.256257445997848e+24	1.3270670518579223e+22
2	8.271414590350508e-303	9.272938339004443e-303	8.646985996095733e-303
8	-1.7330470031600746e-204	-3.4480302657902764e-209	-1.6842396497167515e-204

Iters

Range

Point

4.306451856362919e+21

9.256257445997848e+24

1.3270670518579223e+22

8.271414590350508e-303

9.272938339004443e-303

8.646985996095733e-303

-1.7330470031600746e-204

-3.4480302657902764e-209

-1.6842396497167515e-204

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	156
1	73	156
2	89	156
3	99	156
4	106	156
5	108	156
6	106	156

end3.0ms (0%)

Compiler: Compiled 105 to 79 computations (24.8% saved)

sample2.6s (19.5%)

Algorithm

1×

intervals

Results

536.0ms	5407×	body	128	valid
401.0ms	1101×	body	1024	valid
286.0ms	786×	body	1024	nan
241.0ms	866×	body	512	valid
142.0ms	1574×	body	128	nan
133.0ms	478×	body	512	nan
106.0ms	551×	body	256	valid
49.0ms	275×	body	256	nan
36.0ms	75×	body	2048	valid

Compiler

Compiled 750 to 448 computations (40.3% saved)

Details

analyze1.1s (8.3%)

sample145.0ms (1.1%)

simplify52.0ms (0.4%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series2.6s (19.7%)

rewrite41.0ms (0.3%)

simplify435.0ms (3.3%)

prune839.0ms (6.3%)

localize23.0ms (0.2%)

series318.0ms (2.4%)

rewrite19.0ms (0.1%)

simplify169.0ms (1.3%)

prune349.0ms (2.6%)

localize25.0ms (0.2%)

series249.0ms (1.9%)

rewrite2.0ms (0%)

simplify110.0ms (0.8%)

prune693.0ms (5.2%)

localize26.0ms (0.2%)

series481.0ms (3.6%)

rewrite2.0ms (0%)

simplify142.0ms (1.1%)

prune821.0ms (6.1%)

regimes1.8s (13.4%)

bsearch252.0ms (1.9%)

simplify7.0ms (0.1%)

end3.0ms (0%)

sample2.6s (19.5%)

Profiling