Details

analyze1.2s (6.3%)

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)

sample3.3s (17.6%)

Results

916.0ms	5520×	body	128	valid
647.0ms	1181×	body	1024	valid
446.0ms	838×	body	1024	invalid
379.0ms	930×	body	512	valid
271.0ms	529×	body	512	invalid
233.0ms	1507×	body	128	invalid
167.0ms	541×	body	256	valid
78.0ms	290×	body	256	invalid
54.0ms	84×	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

prune3.0ms (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

45.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.6b	(/.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)

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)
✓	15.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	22.5b	(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 (10.1%)

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))))
309.0ms	(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))
4.0ms	(*.f64 (sqrt.f64 2) t)

rewrite40.0ms (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:

15.0ms	(/.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	(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))
3.0ms	(*.f64 (sqrt.f64 2) t)

simplify429.0ms (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

prune775.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	250	8	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	8	259

Error

7.5b

Counts

259 → 8

Alt Table

Status	Error	Program
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	37.8b	(/.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))))))
	40.8b	(/.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)))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	50.3b	(.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)))))))
	63.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)) l))
▶	36.0b	(/.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))))))))))

Compiler

Compiled 42197 to 31112 computations (26.3% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	20.0b	(/.f64 (.f64 t t) (.f64 x x))
✓	21.2b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	30.7b	(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)))))))))

series673.0ms (3.6%)

Counts

4 → 104

Calls

4 calls:

574.0ms	(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))
32.0ms	(/.f64 (.f64 t t) (.f64 x x))
30.0ms	(/.f64 (.f64 l l) (.f64 x x))

rewrite23.0ms (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:

7.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (*.f64 t t) (pow.f64 x 3))
5.0ms	(/.f64 (.f64 l l) (.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)))))))))

simplify179.0ms (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

prune430.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Error

0.8b

Counts

196 → 10

Alt Table

Status	Error	Program
	42.9b	(/.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 (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))))))))) 3)))
	40.8b	(/.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)))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.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))))))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	37.8b	(/.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))))))
	54.7b	(/.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))))))))
	52.2b	(/.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)))))))
▶	36.0b	(/.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 (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 (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 24704 to 15142 computations (38.7% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	13.5b	(/.f64 (.f64 l l) (.f64 x x))
	20.0b	(/.f64 (.f64 t t) (.f64 x x))
	21.2b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	30.7b	(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)))))))))

series570.0ms (3.1%)

Counts

1 → 32

Calls

1 calls:

567.0ms

(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)))))))))

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 (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)))))))))

simplify147.0ms (0.8%)

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

prune1.0s (5.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	375	1	376
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	375	11	386

Error

0.7b

Counts

386 → 11

Alt Table

Status	Error	Program
	42.9b	(/.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 (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))))))))) 3)))
	40.8b	(/.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)))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.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))))))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	37.8b	(/.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))))))
	54.7b	(/.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))))))))
▶	36.1b	(/.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 (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 (.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))))
	52.2b	(/.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)))))))
✓	36.0b	(/.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 (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 (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 69312 to 37334 computations (46.1% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	20.0b	(/.f64 (.f64 t t) (.f64 x x))
	21.2b	(/.f64 (*.f64 t t) (pow.f64 x 3))
	30.7b	(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)))))))))
✓	31.6b	(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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (*.f64 l l) x)))))))))

series1.0s (5.6%)

Counts

1 → 36

Calls

1 calls:

1.0s

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

rewrite21.0ms (0.1%)

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

simplify299.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

970×	`times-frac_binary64`
948×	`fma-def_binary64`
311×	`*-commutative_binary64`
222×	`+-commutative_binary64`
186×	`associate-+r+_binary64`

Counts

49 → 87

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	831	22079
1	2926	22015
2	5053	22015

prune2.5s (13.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	489	11	500

Error

0.7b

Counts

500 → 11

Alt Table

Status	Error	Program
	42.9b	(/.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 (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))))))))) 3)))
	40.8b	(/.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)))
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (exp.f64 (log.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))))))))))))
	42.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (pow.f64 t 2))))
	39.0b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	37.8b	(/.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))))))
	54.7b	(/.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))))))))
✓	36.1b	(/.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 (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 (.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (+.f64 (/.f64 (.f64 l l) (pow.f64 x 3)) (fma.f64 t t (/.f64 (.f64 l l) x))))))))))))))
	52.2b	(/.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)))))))
✓	36.0b	(/.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 (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 (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 150437 to 85431 computations (43.2% saved)

regimes1.8s (9.5%)

Accuracy

Total 10.6b remaining (95.7%)

Threshold costs 0b (0%)

Counts

78 → 8

Compiler

Compiled 36160 to 20839 computations (42.4% saved)

bsearch1.7s (9.2%)

Steps

Iters	Range		Point
9	4.927547754811477e-50	5.222058546902677e-43	5.140420865775031e-43
4	8.323539737805838e-203	1.250201860997097e-202	8.418248280997763e-203
7	9.561890316620867e-277	2.8180299637923408e-275	2.7904332859958544e-275
9	-1.2277242586577986e-222	-3.0724542176165685e-232	-1.2062010810487966e-222
10	-1.432676743906907e-186	-1.6680561949275367e-196	-1.4178637038882688e-186
7	-3.0249216193976242e-152	-1.901639390264525e-154	-1.9442302404542524e-154
10	-1.8970513977058847e+25	-14188174178012.344	-5.617995743088974e+23

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-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	81	464
1	103	464
2	112	464
3	117	464
4	119	464
5	117	464

end400.0ms (2.2%)

Compiler: Compiled 1207 to 689 computations (42.9% saved)

Details

analyze1.2s (6.3%)

sample3.3s (17.6%)

simplify51.0ms (0.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series1.9s (10.1%)

rewrite40.0ms (0.2%)

simplify429.0ms (2.3%)

prune775.0ms (4.2%)

localize31.0ms (0.2%)

series673.0ms (3.6%)

rewrite23.0ms (0.1%)

simplify179.0ms (1%)

prune430.0ms (2.3%)

localize32.0ms (0.2%)

series570.0ms (3.1%)

rewrite2.0ms (0%)

simplify147.0ms (0.8%)

prune1.0s (5.6%)

localize45.0ms (0.2%)

series1.0s (5.6%)

rewrite21.0ms (0.1%)

simplify299.0ms (1.6%)

prune2.5s (13.6%)

regimes1.8s (9.5%)

bsearch1.7s (9.2%)

simplify11.0ms (0.1%)

end400.0ms (2.2%)

Profiling