Details

analyze1.1s (6.9%)

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)

sample153.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	181×	body	128	valid
15.0ms	41×	body	1024	valid
13.0ms	29×	body	1024	nan
7.0ms	26×	body	512	nan
7.0ms	25×	body	512	valid
5.0ms	55×	body	128	nan
2.0ms	11×	body	256	nan
1.0ms	3×	body	2048	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify52.0ms (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

40.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.6b	(/.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 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (*.f64 l l)))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	14.4b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	19.6b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series471.0ms (3%)

Counts

4 → 120

Calls

4 calls:

331.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
82.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
54.0ms	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (*.f64 l l)))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
40×	`associate-l_binary64`
29×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 116

Calls

4 calls:

10.0ms	(.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (*.f64 l l)))
10.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
8.0ms	(-.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)

simplify351.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
688×	`times-frac_binary64`
268×	`*-commutative_binary64`
198×	`+-commutative_binary64`
156×	`associate-+r+_binary64`

Counts

236 → 283

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	798	16084
1	2470	15103
2	4976	15103
3	5003	15103

prune1.4s (9.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	8	284

Error

5.6b

Counts

284 → 8

Alt Table

Status	Error	Program
▶	31.6b	(/.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))))))))
	40.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (fma.f64 2 (/.f64 x (-.f64 x 1)) (/.f64 2 (-.f64 x 1))))))
	62.9b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)))))
	39.9b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (.f64 (.f64 l l) (.f64 l l))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	40.4b	(/.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)))))
	46.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 2 (/.f64 (.f64 (+.f64 1 x) (pow.f64 t 2)) (-.f64 x 1))) (.f64 l l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (fma.f64 2 (/.f64 x (-.f64 x 1)) (/.f64 2 (-.f64 x 1)))))))

Compiler

Compiled 21224 to 14444 computations (31.9% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.8b	(/.f64 (*.f64 t t) x)
✓	12.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.3b	(/.f64 (.f64 t t) (.f64 x x))
✓	25.7b	(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)))))))

series635.0ms (4.1%)

Counts

4 → 108

Calls

4 calls:

493.0ms	(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)))))))
63.0ms	(/.f64 (.f64 l l) (.f64 x x))
57.0ms	(/.f64 (.f64 t t) (.f64 x x))
21.0ms	(/.f64 (*.f64 t t) x)

rewrite39.0ms (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:

9.0ms	(/.f64 (.f64 t t) (.f64 x x))
9.0ms	(/.f64 (.f64 l l) (.f64 x x))
8.0ms	(/.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)))))))

simplify318.0ms (2%)

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

prune287.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	173	10	183

Error

0.2b

Counts

183 → 10

Alt Table

Status	Error	Program
	40.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
▶	31.8b	(/.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))))))))))
✓	31.6b	(/.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))))))))
	39.5b	(/.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))))))))))
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (.f64 (.f64 l l) (.f64 l l))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	62.9b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)))))
	46.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 2 (/.f64 (.f64 (+.f64 1 x) (pow.f64 t 2)) (-.f64 x 1))) (.f64 l l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (fma.f64 2 (/.f64 x (-.f64 x 1)) (/.f64 2 (-.f64 x 1)))))))

Compiler

Compiled 15347 to 8769 computations (42.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.8b	(/.f64 (*.f64 t t) x)
	12.5b	(/.f64 (.f64 l l) (.f64 x x))
	17.3b	(/.f64 (.f64 t t) (.f64 x x))
✓	25.7b	(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)))))))

series254.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

254.0ms

(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)))))))

simplify109.0ms (0.7%)

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

prune595.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	349	1	350
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	350	10	360

Error

0.2b

Counts

360 → 10

Alt Table

Status	Error	Program
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (.f64 (.f64 l l) (.f64 l l))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
▶	31.8b	(/.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))))))))))))
	40.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
✓	31.8b	(/.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))))))))))
✓	31.6b	(/.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))))))))
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	62.9b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)))))
	46.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 2 (/.f64 (.f64 (+.f64 1 x) (pow.f64 t 2)) (-.f64 x 1))) (.f64 l l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (fma.f64 2 (/.f64 x (-.f64 x 1)) (/.f64 2 (-.f64 x 1)))))))

Compiler

Compiled 42567 to 19965 computations (53.1% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	12.5b	(/.f64 (.f64 l l) (.f64 x x))
	17.3b	(/.f64 (.f64 t t) (.f64 x x))
	25.7b	(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)))))))
✓	26.7b	(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)))))))

series475.0ms (3%)

Counts

1 → 36

Calls

1 calls:

474.0ms

(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)))))))

simplify149.0ms (1%)

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

prune986.0ms (6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	361	1	362
Fresh	0	7	7
Picked	0	1	1
Done	1	1	2
Total	362	10	372

Error

0.2b

Counts

372 → 10

Alt Table

Status	Error	Program
	52.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) (.f64 (.f64 l l) (.f64 l l))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
✓	31.8b	(/.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))))))))))))
	32.6b	(/.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 (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))))))))))))))
	40.5b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
✓	31.6b	(/.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))))))))
	54.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	62.9b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)))))
	46.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 2 (/.f64 (.f64 (+.f64 1 x) (pow.f64 t 2)) (-.f64 x 1))) (.f64 l l))))
	36.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (fma.f64 2 (/.f64 x (-.f64 x 1)) (/.f64 2 (-.f64 x 1)))))))

Compiler

Compiled 71403 to 36489 computations (48.9% saved)

regimes2.3s (14.5%)

Accuracy

Total 10.6b remaining (95%)

Threshold costs 0b (0%)

Counts

78 → 5

Compiler

Compiled 27452 to 15872 computations (42.2% saved)

bsearch873.0ms (5.6%)

Steps

Iters	Range		Point
7	2.097852923601075e-48	4.889114202412453e-47	4.810710790881342e-47
9	3.3291902450569374e-122	1.449642485162383e-115	3.3813144302125017e-122
6	1.6005248398764724e-265	1.6366219125455008e-264	1.6105793316811791e-264
8	-6.902348981073293e-65	-1.9465209104279952e-69	-6.790049380025751e-65

Compiler

Compiled 4 to 3 computations (25% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	204
1	70	204
2	78	204
3	83	204
4	88	204
5	90	204
6	88	204

end4.0ms (0%)

Compiler: Compiled 138 to 90 computations (34.8% saved)

sample4.9s (31.4%)

Algorithm

1×

intervals

Results

1.0s	5382×	body	128	valid
804.0ms	1134×	body	1024	valid
595.0ms	861×	body	1024	nan
470.0ms	889×	body	512	valid
290.0ms	1619×	body	128	nan
252.0ms	486×	body	512	nan
195.0ms	523×	body	256	valid
100.0ms	291×	body	256	nan
66.0ms	72×	body	2048	valid

Compiler

Compiled 662 to 376 computations (43.2% saved)

Details

analyze1.1s (6.9%)

sample153.0ms (1%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series471.0ms (3%)

rewrite41.0ms (0.3%)

simplify351.0ms (2.3%)

prune1.4s (9.2%)

localize43.0ms (0.3%)

series635.0ms (4.1%)

rewrite39.0ms (0.2%)

simplify318.0ms (2%)

prune287.0ms (1.8%)

localize23.0ms (0.1%)

series254.0ms (1.6%)

rewrite2.0ms (0%)

simplify109.0ms (0.7%)

prune595.0ms (3.8%)

localize38.0ms (0.2%)

series475.0ms (3%)

rewrite2.0ms (0%)

simplify149.0ms (1%)

prune986.0ms (6.3%)

regimes2.3s (14.5%)

bsearch873.0ms (5.6%)

simplify16.0ms (0.1%)

end4.0ms (0%)

sample4.9s (31.4%)

Profiling