Details

analyze1.6s (6.4%)

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
6.2%	68.6%	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)

sample5.1s (19.8%)

Results

1.5s	5499×	body	128	valid
1.0s	1163×	body	1024	valid
749.0ms	820×	body	1024	invalid
583.0ms	947×	body	512	valid
387.0ms	1604×	body	128	invalid
310.0ms	489×	body	512	invalid
239.0ms	577×	body	256	valid
125.0ms	306×	body	256	invalid
68.0ms	70×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify86.0ms (0.3%)

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

prune13.0ms (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

43.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.3b	(/.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)

localize39.0ms (0.2%)

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))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	13.5b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	20.5b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series3.7s (14.1%)

Counts

4 → 120

Calls

4 calls:

2.8s	(/.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))))
662.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
156.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
7.0ms	(*.f64 (sqrt.f64 2) t)

rewrite85.0ms (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:

30.0ms	(/.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))))
18.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
17.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
7.0ms	(*.f64 (sqrt.f64 2) t)

simplify773.0ms (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

prune1.8s (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	249	9	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	250	9	259

Error

6.0b

Counts

259 → 9

Alt Table

Status	Error	Program
	40.4b	(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
	39.6b	(/.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)))
	40.0b	(/.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))))))
	62.5b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 t (sqrt.f64 2)) l))
	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)))))))
	40.0b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
▶	31.3b	(/.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))))))))
	43.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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 42239 to 31150 computations (26.3% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.9b	(/.f64 (*.f64 t t) x)
✓	14.8b	(/.f64 (.f64 l l) (.f64 x x))
✓	19.2b	(/.f64 (.f64 t t) (.f64 x x))
✓	27.1b	(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)))))))

series604.0ms (2.3%)

Counts

4 → 108

Calls

4 calls:

462.0ms	(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)))))))
59.0ms	(/.f64 (.f64 l l) (.f64 x x))
58.0ms	(/.f64 (.f64 t t) (.f64 x x))
23.0ms	(/.f64 (*.f64 t t) x)

rewrite42.0ms (0.2%)

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:

10.0ms	(/.f64 (.f64 l l) (.f64 x x))
10.0ms	(/.f64 (.f64 t t) (.f64 x x))
7.0ms	(/.f64 (*.f64 t t) x)
2.0ms	(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)))))))

simplify344.0ms (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

prune642.0ms (2.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	168	7	175
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	170	14	184

Error

0.4b

Counts

184 → 14

Alt Table

Status	Error	Program
	40.4b	(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
	39.6b	(/.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)))
	39.1b	(/.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))))))))))
	40.0b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	31.3b	(/.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))))))))
	40.0b	(/.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))))))
	62.5b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 t (sqrt.f64 2)) l))
▶	31.4b	(/.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))))))))))
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.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))))))) 3)))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) l))))))
	43.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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 15599 to 8955 computations (42.6% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	9.9b	(/.f64 (*.f64 t t) x)
	14.8b	(/.f64 (.f64 l l) (.f64 x x))
	19.2b	(/.f64 (.f64 t t) (.f64 x x))
✓	27.1b	(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)))))))

series421.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

420.0ms

(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)))))))

rewrite3.0ms (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:

2.0ms

(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)))))))

simplify207.0ms (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

prune1.5s (5.6%)

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

0.4b

Counts

364 → 14

Alt Table

Status	Error	Program
	40.4b	(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
	39.6b	(/.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)))
▶	39.1b	(/.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))))))))))
	40.0b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	31.3b	(/.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))))))))
	40.0b	(/.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))))))
	62.5b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 t (sqrt.f64 2)) l))
✓	31.4b	(/.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))))))))))
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.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))))))) 3)))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) l))))))
	43.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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 42829 to 20151 computations (53% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	14.8b	(/.f64 (.f64 l l) (.f64 x x))
	19.2b	(/.f64 (.f64 t t) (.f64 x x))
	27.1b	(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)))))))
✓	36.9b	(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)))))))))

series488.0ms (1.9%)

Counts

1 → 36

Calls

1 calls:

487.0ms

(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)))))))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

16.0ms

(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)))))))))

simplify258.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

48 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	8165
1	1377	6520
2	5016	6520

prune2.8s (10.8%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	519	2	521
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	519	16	535

Error

0.4b

Counts

535 → 16

Alt Table

Status	Error	Program
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	31.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.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))))))) (cbrt.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))))))))))
	40.4b	(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
	39.6b	(/.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)))
✓	39.1b	(/.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))))))))))
	40.0b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	53.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	31.3b	(/.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))))))))
	40.0b	(/.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))))))
	62.5b	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1))) (/.f64 (.f64 t (sqrt.f64 2)) l))
✓	31.4b	(/.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))))))))))
	40.5b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.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)))))))) 1/3))
	39.1b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.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))))))) 3)))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	53.9b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) l))))))
	43.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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 85256 to 40065 computations (53% saved)

regimes3.5s (13.7%)

Accuracy

Total 11.7b remaining (95.7%)

Threshold costs 0b (0%)

Counts

95 → 6

Compiler

Compiled 34719 to 20723 computations (40.3% saved)

bsearch961.0ms (3.7%)

Steps

Iters	Range		Point
9	215754.17723668477	563379465749.548	229211672411.04373
10	-1.523215747200925e-211	-1.1008079058953385e-229	-1.2714670369176393e-211
9	-1.8607615226984031e-171	-2.0308454765202666e-176	-1.8440714154310572e-171
4	-3.909229599474971e-84	-2.3422443549921814e-84	-2.391212643882269e-84
10	-5.351818877033207e+36	-4.6027262382850696e+26	-3.2023462066894274e+36

Compiler

Compiled 4 to 3 computations (25% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
12×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	326
1	110	326
2	125	326
3	133	326
4	136	326
5	134	326

end697.0ms (2.7%)

Compiler: Compiled 1224 to 681 computations (44.4% saved)

Details

analyze1.6s (6.4%)

sample5.1s (19.8%)

simplify86.0ms (0.3%)

prune13.0ms (0%)

localize39.0ms (0.2%)

series3.7s (14.1%)

rewrite85.0ms (0.3%)

simplify773.0ms (3%)

prune1.8s (7.1%)

localize43.0ms (0.2%)

series604.0ms (2.3%)

rewrite42.0ms (0.2%)

simplify344.0ms (1.3%)

prune642.0ms (2.5%)

localize39.0ms (0.1%)

series421.0ms (1.6%)

rewrite3.0ms (0%)

simplify207.0ms (0.8%)

prune1.5s (5.6%)

localize48.0ms (0.2%)

series488.0ms (1.9%)

rewrite20.0ms (0.1%)

simplify258.0ms (1%)

prune2.8s (10.8%)

regimes3.5s (13.7%)

bsearch961.0ms (3.7%)

simplify10.0ms (0%)

end697.0ms (2.7%)

Profiling