Details

analyze1.1s (9.3%)

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)

sample3.5s (29.2%)

Results

996.0ms	5453×	body	128	valid
706.0ms	1187×	body	1024	valid
479.0ms	826×	body	1024	invalid
416.0ms	990×	body	512	valid
275.0ms	1578×	body	128	invalid
259.0ms	507×	body	512	invalid
170.0ms	563×	body	256	valid
80.0ms	270×	body	256	invalid
50.0ms	63×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% 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

45.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.2b	(/.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))))
✓	0.5b	(*.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))
✓	20.2b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.9s (15.5%)

Counts

4 → 120

Calls

4 calls:

1.5s	(/.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))))
318.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
78.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

rewrite45.0ms (0.4%)

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:

13.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
13.0ms	(/.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))))
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)

simplify397.0ms (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

prune774.0ms (6.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	252	6	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	253	6	259

Error

5.8b

Counts

259 → 6

Alt Table

Status	Error	Program
	37.4b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	37.0b	(/.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)))
	44.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (fma.f64 (neg.f64 l) l (.f64 l l)))))
▶	30.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))
	45.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))

Compiler

Compiled 42177 to 31080 computations (26.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))
✓	5.5b	(/.f64 (*.f64 l l) x)
✓	10.3b	(/.f64 (*.f64 t t) x)
✓	27.2b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))

series188.0ms (1.6%)

Counts

4 → 116

Calls

4 calls:

123.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))
44.0ms	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))
10.0ms	(/.f64 (*.f64 t t) x)
10.0ms	(/.f64 (*.f64 l l) x)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 71

Calls

4 calls:

3.0ms	(/.f64 (*.f64 t t) x)
3.0ms	(/.f64 (*.f64 l l) x)
1.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))
0.0ms	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

531×	`cancel-sign-sub-inv_binary64`
236×	`times-frac_binary64`
236×	`fma-neg_binary64`
205×	`unswap-sqr_binary64`
201×	`sub-neg_binary64`

Counts

187 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	5324
1	771	4853
2	3429	4827
3	4916	4827
4	4975	4827

prune185.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	148	9	157
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	149	14	163

Error

0.3b

Counts

163 → 14

Alt Table

Status	Error	Program
▶	26.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))
	37.0b	(/.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)))
	38.5b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 (/.f64 l (sqrt.f64 x)) (/.f64 l (sqrt.f64 x))) (*.f64 t t))))))
	37.4b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x))))
	45.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	44.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (fma.f64 (neg.f64 l) l (.f64 l l)))))
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
	27.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))) (.f64 t t))))))
	36.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x))) (.f64 (/.f64 (.f64 l l) (.f64 x t)) (sqrt.f64 (/.f64 1 (+.f64 2 (/.f64 4 x))))))))
	30.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)) (.f64 (.f64 t t) (/.f64 4 x))))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)) (.f64 (.f64 t t) (/.f64 4 x)))))))
	40.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)) (.f64 (.f64 t t) (/.f64 4 x)))) 3)))
	41.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))

Compiler

Compiled 7042 to 4237 computations (39.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(+.f64 (/.f64 l (/.f64 x l)) (*.f64 t t))
✓	2.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (*.f64 t t))))
	10.3b	(/.f64 (*.f64 t t) x)
✓	27.2b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (*.f64 t t)))))

series186.0ms (1.5%)

Counts

3 → 104

Calls

3 calls:

122.0ms

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

45.0ms

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

18.0ms

(+.f64 (/.f64 l (/.f64 x l)) (*.f64 t t))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
44×	`fma-def_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

11.0ms

(+.f64 (/.f64 l (/.f64 x l)) (*.f64 t t))

1.0ms

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

0.0ms

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

simplify129.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

566×	`cancel-sign-sub-inv_binary64`
381×	`fma-neg_binary64`
247×	`neg-sub0_binary64`
243×	`neg-mul-1_binary64`
202×	`fma-def_binary64`

Counts

186 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	5146
1	717	4650
2	2933	4469
3	4449	4457
4	5022	4457

prune216.0ms (1.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	197	3	200
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	199	15	214

Error

0.3b

Counts

214 → 15

Alt Table

Status	Error	Program
✓	26.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))
	37.0b	(/.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)))
▶	27.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t))))))
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
	27.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))))
	37.4b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x))))
	45.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	44.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (fma.f64 (neg.f64 l) l (.f64 l l)))))
	27.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))) (.f64 t t))))))
	36.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x))) (.f64 (/.f64 (.f64 l l) (.f64 x t)) (sqrt.f64 (/.f64 1 (+.f64 2 (/.f64 4 x))))))))
	30.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 1 x) (/.f64 l (/.f64 1 l)) (.f64 t t))))))
	40.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)) (.f64 (.f64 t t) (/.f64 4 x)))) 3)))
	41.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))

Compiler

Compiled 8585 to 4797 computations (44.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 l) (cbrt.f64 l))
✓	2.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (.f64 t t))))
	10.3b	(/.f64 (*.f64 t t) x)
✓	27.2b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (.f64 t t)))))

series685.0ms (5.7%)

Counts

3 → 80

Calls

3 calls:

408.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (*.f64 2 (fma.f64 (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t))))

240.0ms

(sqrt.f64 (fma.f64 4 (/.f64 (*.f64 t t) x) (*.f64 2 (fma.f64 (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t)))))

36.0ms

(*.f64 (cbrt.f64 l) (cbrt.f64 l))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

3 → 67

Calls

3 calls:

6.0ms

(*.f64 (cbrt.f64 l) (cbrt.f64 l))

1.0ms

(sqrt.f64 (fma.f64 4 (/.f64 (*.f64 t t) x) (*.f64 2 (fma.f64 (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t)))))

0.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (*.f64 2 (fma.f64 (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t))))

simplify140.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
418×	`cancel-sign-sub-inv_binary64`
217×	`fma-neg_binary64`
211×	`unswap-sqr_binary64`
156×	`neg-mul-1_binary64`

Counts

147 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	4435
1	621	3917
2	2456	3678
3	4575	3655
4	4940	3655
5	4962	3655

prune184.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	171	15	186

Error

0.3b

Counts

186 → 15

Alt Table

Status	Error	Program
✓	26.9b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))
	37.0b	(/.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)))
✓	27.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (/.f64 (cbrt.f64 l) (/.f64 x l)) (*.f64 t t))))))
	54.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
	40.5b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (.f64 t t) (+.f64 2 (/.f64 4 x)) (.f64 2 (/.f64 (.f64 l l) x)))) 3)))
	27.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t))))))))
	37.4b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2)))
	41.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.2b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x))))
	45.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	44.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (fma.f64 (neg.f64 l) l (.f64 l l)))))
	27.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))) (.f64 t t))))))
	36.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x))) (.f64 (/.f64 (.f64 l l) (.f64 x t)) (sqrt.f64 (/.f64 1 (+.f64 2 (/.f64 4 x))))))))
	30.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 (/.f64 1 x) (/.f64 l (/.f64 1 l)) (.f64 t t))))))
	41.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))

Compiler

Compiled 7414 to 3895 computations (47.5% saved)

regimes1.7s (14%)

Accuracy

Total 8.6b remaining (95.2%)

Threshold costs 0b (0%)

Counts

115 → 3

Compiler

Compiled 30146 to 21145 computations (29.9% saved)

bsearch159.0ms (1.3%)

Steps

Iters	Range		Point
9	1.446461825908414e+147	1.6782736424617207e+152	3.4585179810977915e+148
10	-3.4359178588279094e+139	-1.8851258834237482e+128	-3.8721814473273005e+137

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-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	35	114
1	52	114
2	61	114
3	66	114
4	68	114
5	66	114

end277.0ms (2.3%)

Compiler: Compiled 659 to 443 computations (32.8% saved)

Details

analyze1.1s (9.3%)

sample3.5s (29.2%)

simplify52.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series1.9s (15.5%)

rewrite45.0ms (0.4%)

simplify397.0ms (3.3%)

prune774.0ms (6.4%)

localize15.0ms (0.1%)

series188.0ms (1.6%)

rewrite11.0ms (0.1%)

simplify133.0ms (1.1%)

prune185.0ms (1.5%)

localize15.0ms (0.1%)

series186.0ms (1.5%)

rewrite19.0ms (0.2%)

simplify129.0ms (1.1%)

prune216.0ms (1.8%)

localize21.0ms (0.2%)

series685.0ms (5.7%)

rewrite10.0ms (0.1%)

simplify140.0ms (1.2%)

prune184.0ms (1.5%)

regimes1.7s (14%)

bsearch159.0ms (1.3%)

simplify4.0ms (0%)

end277.0ms (2.3%)

Profiling