Details

analyze1.3s (8.5%)

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 (22.8%)

Results

958.0ms	5499×	body	128	valid
735.0ms	1163×	body	1024	valid
467.0ms	820×	body	1024	invalid
419.0ms	947×	body	512	valid
267.0ms	1604×	body	128	invalid
221.0ms	489×	body	512	invalid
180.0ms	577×	body	256	valid
94.0ms	306×	body	256	invalid
66.0ms	70×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% 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

43.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.0b	(/.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))))

Compiler

Compiled 114 to 72 computations (36.8% saved)

localize17.0ms (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)
✓	13.5b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	19.7b	(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 (12.4%)

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))))
322.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
79.0ms	(-.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)

rewrite38.0ms (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:

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))))
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 (2.6%)

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

prune794.0ms (5.2%)

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

6.1b

Counts

259 → 9

Alt Table

Status	Error	Program
	47.0b	(.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)))))))
	39.3b	(/.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))))))
	39.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))) t))
	39.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
▶	30.8b	(/.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))))))))
	43.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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))))
	63.5b	(.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))
	40.6b	(/.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)))
	40.9b	(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 42271 to 31178 computations (26.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.5b	(/.f64 (*.f64 t t) x)
✓	14.8b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	26.3b	(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)))))))

series316.0ms (2.1%)

Counts

4 → 108

Calls

4 calls:

243.0ms	(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)))))))
31.0ms	(/.f64 (.f64 l l) (.f64 x x))
31.0ms	(/.f64 (.f64 t t) (.f64 x x))
11.0ms	(/.f64 (*.f64 t t) x)

rewrite18.0ms (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:

5.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (.f64 l l) (.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)))))))

simplify164.0ms (1.1%)

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

prune303.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	167	8	175
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	170	14	184

Error

0.4b

Counts

184 → 14

Alt Table

Status	Error	Program
	39.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.9b	(/.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))) 3)))
✓	30.8b	(/.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))))))))
	53.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	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))
	38.9b	(/.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))))))))))
	43.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) l))))))
	53.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	39.3b	(/.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)))))))
	63.5b	(.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))
▶	30.8b	(/.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))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	40.9b	(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 15627 to 8977 computations (42.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	8.5b	(/.f64 (*.f64 t t) x)
	14.8b	(/.f64 (.f64 l l) (.f64 x x))
	17.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	26.3b	(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)))))))

series244.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

244.0ms

(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)))))))

simplify106.0ms (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

prune633.0ms (4.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	350	14	364

Error

0.4b

Counts

364 → 14

Alt Table

Status	Error	Program
	39.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.9b	(/.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))) 3)))
✓	30.8b	(/.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))))))))
	53.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	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))
▶	38.9b	(/.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))))))))))
	43.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) l))))))
	53.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	39.3b	(/.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)))))))
	63.5b	(.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))
✓	30.8b	(/.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))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	40.9b	(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 42857 to 20173 computations (52.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	14.8b	(/.f64 (.f64 l l) (.f64 x x))
	17.9b	(/.f64 (.f64 t t) (.f64 x x))
	26.3b	(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)))))))
✓	36.4b	(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)))))))))

series247.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

246.0ms

(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)))))))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

7.0ms

(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)))))))))

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-def_binary64`
289×	`associate-/r*_binary64`
281×	`associate-r_binary64`
254×	`associate-l_binary64`
221×	`times-frac_binary64`

Counts

48 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	8165
1	1377	6520
2	5016	6520

prune1.3s (8.3%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	519	2	521
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	519	16	535

Error

0.4b

Counts

535 → 16

Alt Table

Status	Error	Program
	39.3b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) (sqrt.f64 2))
	38.9b	(/.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 (.f64 2 (+.f64 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 t t (/.f64 (.f64 l l) x))))))) 3)))
✓	30.8b	(/.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))))))))
	53.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	31.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.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))))))))))
	54.0b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 2 (.f64 (/.f64 (.f64 t t) (.f64 l (.f64 x x))) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))))) (fma.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x))))) (+.f64 (.f64 2 (/.f64 (.f64 t t) (.f64 l x))) (/.f64 (*.f64 t t) 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))
✓	38.9b	(/.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))))))))))
	43.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) t)) (cbrt.f64 (.f64 (sqrt.f64 2) t))) (cbrt.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))))
	53.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	40.3b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.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)))))))) 1/3))
	39.3b	(/.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)))))))
	63.5b	(.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))
✓	30.8b	(/.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))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	40.9b	(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 85270 to 40076 computations (53% saved)

regimes2.4s (16%)

Accuracy

Total 11.9b remaining (96.5%)

Threshold costs 0b (0%)

Counts

98 → 7

Compiler

Compiled 37785 to 23085 computations (38.9% saved)

bsearch965.0ms (6.3%)

Steps

Iters	Range		Point
9	215754.17723668477	563379465749.548	551901859535.9883
7	-5.632551639344985e-256	-1.7950542347399547e-257	-5.528925291641549e-256
10	-1.523215747200925e-211	-1.1008079058953385e-229	-1.1250698168828552e-229
9	-1.8607615226984031e-171	-2.0308454765202666e-176	-1.8440714154310572e-171
4	-3.909229599474971e-84	-2.3422443549921814e-84	-2.391212643882269e-84
9	-4.0060432756404846e+43	-2.9161180078603696e+35	-3.7115896234152697e+43

Compiler

Compiled 4 to 3 computations (25% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
22×	`+-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	92	416
1	133	416
2	160	416
3	180	416
4	197	416
5	208	416
6	214	416
7	217	416
8	218	416
9	216	416

end428.0ms (2.8%)

Compiler: Compiled 1356 to 766 computations (43.5% saved)

Iter	Nodes	Cost
0	92	416
1	133	416
2	160	416
3	180	416
4	197	416
5	208	416
6	214	416
7	217	416
8	218	416
9	216	416

Iter	Nodes	Cost
0	92	416
1	133	416
2	160	416
3	180	416
4	197	416
5	208	416
6	214	416
7	217	416
8	218	416
9	216	416

Details

analyze1.3s (8.5%)

sample3.5s (22.8%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series1.9s (12.4%)

rewrite38.0ms (0.2%)

simplify395.0ms (2.6%)

prune794.0ms (5.2%)

localize20.0ms (0.1%)

series316.0ms (2.1%)

rewrite18.0ms (0.1%)

simplify164.0ms (1.1%)

prune303.0ms (2%)

localize24.0ms (0.2%)

series244.0ms (1.6%)

rewrite2.0ms (0%)

simplify106.0ms (0.7%)

prune633.0ms (4.1%)

localize24.0ms (0.2%)

series247.0ms (1.6%)

rewrite9.0ms (0.1%)

simplify110.0ms (0.7%)

prune1.3s (8.3%)

regimes2.4s (16%)

bsearch965.0ms (6.3%)

simplify18.0ms (0.1%)

end428.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	92	416
1	133	416
2	160	416
3	180	416
4	197	416
5	208	416
6	214	416
7	217	416
8	218	416
9	216	416