Details

analyze1.1s (6.6%)

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)

sample75.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	162×	body	128	valid
14.0ms	35×	body	1024	valid
10.0ms	36×	body	512	valid
8.0ms	22×	body	1024	nan
4.0ms	17×	body	512	nan
4.0ms	20×	body	256	valid
3.0ms	36×	body	128	nan
2.0ms	3×	body	2048	valid
1.0ms	4×	body	256	nan

Compiler

Compiled 64 to 44 computations (31.3% saved)

simplify50.0ms (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

44.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.7b	(/.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)

localize16.0ms (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)
✓	14.6b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	20.4b	(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 (11%)

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))))
315.0ms	(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))
4.0ms	(*.f64 (sqrt.f64 2) t)

rewrite41.0ms (0.2%)

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:

14.0ms	(/.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))))
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)))
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)

simplify395.0ms (2.3%)

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

prune819.0ms (4.8%)

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

7.2b

Counts

259 → 9

Alt Table

Status	Error	Program
	63.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1)) l)))
	38.2b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	39.4b	(/.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)))
	40.3b	(/.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))))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
▶	33.9b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	53.7b	(exp.f64 (log.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))))))
	44.2b	(/.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)))))
	39.8b	(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 42305 to 31182 computations (26.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	15.8b	(/.f64 (.f64 l l) (.f64 x x))
✓	19.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	20.4b	(/.f64 (.f64 t t) (.f64 x x))
✓	29.0b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

series689.0ms (4.1%)

Counts

4 → 104

Calls

4 calls:

592.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))
35.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
31.0ms	(/.f64 (.f64 l l) (.f64 x x))
30.0ms	(/.f64 (.f64 t t) (.f64 x x))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
14×	`associate-/r*_binary64`
14×	`times-frac_binary64`
14×	`div-exp_binary64`

Counts

4 → 106

Calls

4 calls:

5.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
5.0ms	(/.f64 (.f64 l l) (.f64 x x))
5.0ms	(/.f64 (.f64 t t) (.f64 x 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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

simplify185.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/r*_binary64`
671×	`fma-def_binary64`
519×	`associate-/l*_binary64`
217×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

210 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	680	14444
1	1992	12162
2	5408	12162

prune478.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	186	11	197

Error

0.4b

Counts

197 → 11

Alt Table

Status	Error	Program
	52.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	40.3b	(/.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))))
	39.4b	(/.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)))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
✓	33.9b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	53.7b	(exp.f64 (log.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))))))
	38.2b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
▶	34.0b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	34.2b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))

Compiler

Compiled 25097 to 15338 computations (38.9% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	15.8b	(/.f64 (.f64 l l) (.f64 x x))
	19.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
	20.4b	(/.f64 (.f64 t t) (.f64 x x))
✓	29.8b	(cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

series1.1s (6.6%)

Counts

1 → 36

Calls

1 calls:

1.1s

(cbrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

simplify285.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

970×	`times-frac_binary64`
947×	`fma-def_binary64`
311×	`*-commutative_binary64`
221×	`+-commutative_binary64`
185×	`associate-+r+_binary64`

Counts

49 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	831	22095
1	2924	22063
2	5050	22063

prune1.7s (10.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	374	2	376
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	375	12	387

Error

0.4b

Counts

387 → 12

Alt Table

Status	Error	Program
	52.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	40.3b	(/.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))))
	59.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))))) (.f64 2 (log.f64 (/.f64 1 l))))))) (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	39.4b	(/.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)))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
✓	33.9b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	38.2b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
✓	34.0b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
▶	34.2b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))

Compiler

Compiled 99271 to 61437 computations (38.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	15.8b	(/.f64 (.f64 l l) (.f64 x x))
	19.1b	(/.f64 (*.f64 t t) (pow.f64 x 3))
	20.4b	(/.f64 (.f64 t t) (.f64 x x))
✓	29.0b	(sqrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

series654.0ms (3.9%)

Counts

1 → 32

Calls

1 calls:

654.0ms

(sqrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (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:

1.0ms

(sqrt.f64 (fma.f64 (/.f64 (*.f64 t t) (*.f64 x x)) 4 (fma.f64 (/.f64 (*.f64 t t) x) 4 (fma.f64 (/.f64 (*.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (*.f64 l l) (*.f64 x x)) (*.f64 2 (+.f64 (/.f64 (*.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

simplify160.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
296×	`associate-l_binary64`
262×	`associate-*r/_binary64`

Counts

47 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	565	12538
1	1768	10428
2	5437	10428

prune2.8s (16.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	564	0	564
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	564	12	576

Error

0.4b

Counts

576 → 12

Alt Table

Status	Error	Program
	52.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))
	40.3b	(/.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))))
	59.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (+.f64 (.f64 2 (/.f64 1 x)) (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))))) (.f64 2 (log.f64 (/.f64 1 l))))))) (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	39.4b	(/.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)))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	53.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
✓	33.9b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (fma.f64 (/.f64 (.f64 l l) (.f64 (.f64 x x) t)) (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (fma.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 4 (.f64 x x))))))) (+.f64 (/.f64 (.f64 l l) (.f64 (pow.f64 x 3) t)) (/.f64 (.f64 l l) (.f64 x t))))))))
	38.2b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
✓	34.0b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
✓	34.2b	(/.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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))
	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (fabs.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x)))))))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 (.f64 t t) (.f64 x x)) 4 (fma.f64 (/.f64 (.f64 t t) x) 4 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (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 (fma.f64 (/.f64 (.f64 t t) (pow.f64 x 3)) 4 (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))

Compiler

Compiled 134346 to 66806 computations (50.3% saved)

regimes1.1s (6.3%)

Accuracy

Total 10.7b remaining (95.6%)

Threshold costs 0b (0%)

Counts

59 → 5

Compiler

Compiled 22184 to 13777 computations (37.9% saved)

bsearch465.0ms (2.8%)

Steps

Iters	Range		Point
7	1.8067001225355974e+21	4.014674870743059e+22	3.3277568664650287e+22
9	-5.928258331023866e-193	-1.1234603592474926e-200	-5.818528907553507e-193
10	-9.039831643909215e-150	-3.965970309261508e-165	-4.0200485935821406e-165
6	-67212678.75037912	-12938207.674276667	-66516108.83864204

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
11×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	304
1	92	304
2	103	304
3	109	304
4	111	304
5	109	304

end3.0ms (0%)

Compiler: Compiled 204 to 132 computations (35.3% saved)

sample2.8s (16.8%)

Algorithm

1×

intervals

Results

512.0ms	5320×	body	128	valid
453.0ms	1122×	body	1024	valid
308.0ms	849×	body	1024	nan
256.0ms	942×	body	512	valid
141.0ms	1522×	body	128	nan
138.0ms	512×	body	512	nan
100.0ms	549×	body	256	valid
47.0ms	246×	body	256	nan
30.0ms	67×	body	2048	valid

Compiler

Compiled 1171 to 667 computations (43% saved)

Details

analyze1.1s (6.6%)

sample75.0ms (0.4%)

simplify50.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.9s (11%)

rewrite41.0ms (0.2%)

simplify395.0ms (2.3%)

prune819.0ms (4.8%)

localize29.0ms (0.2%)

series689.0ms (4.1%)

rewrite24.0ms (0.1%)

simplify185.0ms (1.1%)

prune478.0ms (2.8%)

localize33.0ms (0.2%)

series1.1s (6.6%)

rewrite2.0ms (0%)

simplify285.0ms (1.7%)

prune1.7s (10.1%)

localize34.0ms (0.2%)

series654.0ms (3.9%)

rewrite3.0ms (0%)

simplify160.0ms (0.9%)

prune2.8s (16.4%)

regimes1.1s (6.3%)

bsearch465.0ms (2.8%)

simplify9.0ms (0.1%)

end3.0ms (0%)

sample2.8s (16.8%)

Profiling