Details

analyze1.1s (6.7%)

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)

sample3.3s (20.6%)

Results

941.0ms	5470×	body	128	valid
629.0ms	1189×	body	1024	valid
451.0ms	791×	body	1024	invalid
422.0ms	975×	body	512	valid
260.0ms	1630×	body	128	invalid
219.0ms	545×	body	512	invalid
205.0ms	563×	body	256	valid
81.0ms	285×	body	256	invalid
44.0ms	59×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify51.0ms (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

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

40.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.8b	(/.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)

localize14.0ms (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))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	11.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	19.1b	(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 (15.9%)

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))))
317.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
81.0ms	(-.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)

rewrite42.0ms (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)

simplify388.0ms (2.4%)

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

prune801.0ms (4.9%)

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

5.8b

Counts

259 → 9

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.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))))
	37.5b	(/.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)))
	47.1b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	39.1b	(/.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))))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))) (.f64 t t))))
▶	31.5b	(/.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))))))))
	40.1b	(/.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)))))
	39.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	63.7b	(neg.f64 (.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)))

Compiler

Compiled 42439 to 31296 computations (26.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.0b	(/.f64 (*.f64 t t) x)
✓	11.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	18.0b	(/.f64 (.f64 t t) (.f64 x x))
✓	26.0b	(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)))))))

series305.0ms (1.9%)

Counts

4 → 108

Calls

4 calls:

232.0ms	(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)))))))
32.0ms	(/.f64 (.f64 l l) (.f64 x x))
30.0ms	(/.f64 (.f64 t t) (.f64 x x))
10.0ms	(/.f64 (*.f64 t t) x)

rewrite17.0ms (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:

4.0ms	(/.f64 (.f64 l l) (.f64 x x))
4.0ms	(/.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)))))))

simplify161.0ms (1%)

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

prune282.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	173	11	184

Error

0.4b

Counts

184 → 11

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.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))))
	37.5b	(/.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)))
	47.1b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	39.1b	(/.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))))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))) (.f64 t t))))
▶	31.6b	(/.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))))))))))
	39.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	31.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (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)))))))) (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))))))))) (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))))))))))
	41.4b	(/.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))))))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))

Compiler

Compiled 15686 to 8975 computations (42.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	9.0b	(/.f64 (*.f64 t t) x)
	11.5b	(/.f64 (.f64 l l) (.f64 x x))
	18.0b	(/.f64 (.f64 t t) (.f64 x x))
✓	26.0b	(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)))))))

series234.0ms (1.4%)

Counts

1 → 36

Calls

1 calls:

234.0ms

(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)))))))

simplify96.0ms (0.6%)

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

prune592.0ms (3.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	349	1	350
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	349	12	361

Error

0.4b

Counts

361 → 12

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.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))))
	37.5b	(/.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)))
	47.1b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	39.1b	(/.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))))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))) (.f64 t t))))
✓	31.6b	(/.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))))))))))
	39.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	31.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (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)))))))) (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))))))))) (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))))))))))
	41.4b	(/.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))))))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
▶	31.6b	(/.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 (.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 (fma.f64 (/.f64 l x) (/.f64 l 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 (fma.f64 (/.f64 l x) (/.f64 l x) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))

Compiler

Compiled 43150 to 20261 computations (53% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	11.5b	(/.f64 (.f64 l l) (.f64 x x))
	18.0b	(/.f64 (.f64 t t) (.f64 x x))
	26.0b	(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)))))))
✓	26.9b	(cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (fma.f64 (/.f64 l x) (/.f64 l x) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))

series450.0ms (2.8%)

Counts

1 → 36

Calls

1 calls:

450.0ms

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

simplify131.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

49 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	563	10670
1	1897	9782
2	5315	9782

prune981.0ms (6.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	361	1	362
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	361	13	374

Error

0.4b

Counts

374 → 13

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.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))))
	37.5b	(/.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)))
	47.1b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	32.4b	(/.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 (.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 (fma.f64 (/.f64 l x) (/.f64 l x) (fma.f64 t t (/.f64 (.f64 l l) x)))))))) (sqrt.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (.f64 2 (fma.f64 (/.f64 l x) (/.f64 l x) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))))
	39.1b	(/.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))))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))) (.f64 t t))))
✓	31.6b	(/.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))))))))))
	39.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	31.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (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)))))))) (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))))))))) (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))))))))))
	41.4b	(/.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))))))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
✓	31.6b	(/.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 (.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 (fma.f64 (/.f64 l x) (/.f64 l 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 (fma.f64 (/.f64 l x) (/.f64 l x) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	56.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))

Compiler

Compiled 71753 to 36658 computations (48.9% saved)

regimes3.5s (21.7%)

Accuracy

Total 9.8b remaining (94.9%)

Threshold costs 0b (0%)

Counts

189 → 6

Compiler

Compiled 59198 to 33728 computations (43% saved)

bsearch649.0ms (4%)

Steps

Iters	Range		Point
10	9.923349407334466e+41	8.467964221546523e+58	1.61647280189764e+54
6	5.933916300750221e-176	2.5231179502886538e-175	5.986192385954492e-176
7	-3.860992951043014e-284	-5.348663396012331e-286	-3.7962369205500905e-284
8	-5.280198255469237e-160	-3.582141876278634e-164	-3.675917657008533e-164
6	-1.7205924140020095e+35	-1.4882281480532921e+34	-1.6738301690329368e+35

Compiler

Compiled 4 to 3 computations (25% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
20×	`+-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	342
1	106	342
2	134	342
3	155	342
4	174	342
5	186	342
6	192	342
7	195	342
8	196	342
9	194	342

end397.0ms (2.4%)

Compiler: Compiled 1300 to 701 computations (46.1% saved)

Iter	Nodes	Cost
0	74	342
1	106	342
2	134	342
3	155	342
4	174	342
5	186	342
6	192	342
7	195	342
8	196	342
9	194	342

Iter	Nodes	Cost
0	74	342
1	106	342
2	134	342
3	155	342
4	174	342
5	186	342
6	192	342
7	195	342
8	196	342
9	194	342

Details

analyze1.1s (6.7%)

sample3.3s (20.6%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series2.6s (15.9%)

rewrite42.0ms (0.3%)

simplify388.0ms (2.4%)

prune801.0ms (4.9%)

localize22.0ms (0.1%)

series305.0ms (1.9%)

rewrite17.0ms (0.1%)

simplify161.0ms (1%)

prune282.0ms (1.7%)

localize23.0ms (0.1%)

series234.0ms (1.4%)

rewrite2.0ms (0%)

simplify96.0ms (0.6%)

prune592.0ms (3.7%)

localize34.0ms (0.2%)

series450.0ms (2.8%)

rewrite2.0ms (0%)

simplify131.0ms (0.8%)

prune981.0ms (6.1%)

regimes3.5s (21.7%)

bsearch649.0ms (4%)

simplify15.0ms (0.1%)

end397.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	74	342
1	106	342
2	134	342
3	155	342
4	174	342
5	186	342
6	192	342
7	195	342
8	196	342
9	194	342