Details

analyze177.0ms (1.7%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample31.0ms (0.3%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify34.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

Compiler

Compiled 114 to 77 computations (32.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 5 (.f64 v v))
✓	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
✓	0.5b	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

series199.0ms (1.9%)

Counts

4 → 60

Calls

4 calls:

161.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
34.0ms	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
3.0ms	(.f64 5 (.f64 v v))
2.0ms	(*.f64 (PI.f64) t)

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
7.0ms	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
4.0ms	(.f64 5 (.f64 v v))
3.0ms	(*.f64 (PI.f64) t)

simplify136.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
489×	`associate-r_binary64`
436×	`times-frac_binary64`
397×	`associate-/r*_binary64`
215×	`associate-/l*_binary64`

Counts

162 → 195

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	339	5940
1	1042	5332
2	4928	5332
3	4937	5332

prune273.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	8	195
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	9	196

Error

0.1b

Counts

196 → 9

Alt Table

Status	Error	Program
	1.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (cbrt.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (-.f64 1 (*.f64 v v))))
	29.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
▶	0.7b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
✓	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
	41.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))) (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
	0.8b	(-.f64 (/.f64 1 (.f64 (PI.f64) (.f64 t (sqrt.f64 2)))) (.f64 5/2 (/.f64 (pow.f64 v 2) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))))
	1.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
	42.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 1 (.f64 5 (.f64 v v)))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))

Compiler

Compiled 9485 to 6177 computations (34.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
✓	0.3b	(.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
✓	0.3b	(.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))

series794.0ms (7.6%)

Counts

3 → 72

Calls

3 calls:

604.0ms

(*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))))

158.0ms

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (-.f64 1 (*.f64 v v))))

32.0ms

(*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))))

rewrite78.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`sqrt-div_binary64`
86×	`associate-*r/_binary64`
37×	`add-cbrt-cube_binary64`
37×	`add-exp-log_binary64`
35×	`flip--_binary64`

Counts

3 → 119

Calls

3 calls:

23.0ms

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (-.f64 1 (*.f64 v v))))

16.0ms

(*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))))

8.0ms

(*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))))

simplify156.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

806×	`times-frac_binary64`
621×	`associate-/r*_binary64`
337×	`associate-/l*_binary64`
186×	`fma-def_binary64`
158×	`*-commutative_binary64`

Counts

191 → 266

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	454	9848
1	1502	8797
2	5178	8797

prune552.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	5	2	7
Picked	0	1	1
Done	1	0	1
Total	289	8	297

Error

0.1b

Counts

297 → 8

Alt Table

Status	Error	Program
	29.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
✓	0.7b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))))
▶	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
	0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (-.f64 1 (*.f64 v v))))
	42.0b	(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 (.f64 v v) 5)) 3) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) 3) (pow.f64 (-.f64 1 (*.f64 v v)) 3))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))

Compiler

Compiled 18189 to 12256 computations (32.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 5 (.f64 v v))
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
✓	0.3b	(.f64 (PI.f64) (.f64 t (sqrt.f64 2)))
✓	0.4b	(*.f64 t (sqrt.f64 2))

series165.0ms (1.6%)

Counts

3 → 24

Calls

3 calls:

157.0ms

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (*.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (-.f64 1 (*.f64 v v))))

5.0ms

(*.f64 (PI.f64) (*.f64 t (sqrt.f64 2)))

3.0ms

(*.f64 t (sqrt.f64 2))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
14×	`cbrt-unprod_binary64`
14×	`prod-exp_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

3 → 84

Calls

3 calls:

16.0ms

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (*.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (-.f64 1 (*.f64 v v))))

4.0ms

(*.f64 (PI.f64) (*.f64 t (sqrt.f64 2)))

4.0ms

(*.f64 t (sqrt.f64 2))

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
441×	`associate-l_binary64`
377×	`associate-r_binary64`
354×	`associate-/r*_binary64`
341×	`times-frac_binary64`

Counts

108 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	4779
1	869	4128
2	4148	3915
3	5062	3915

prune259.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Error

0.1b

Counts

180 → 8

Alt Table

Status	Error	Program
	29.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
✓	0.7b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))))
✓	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
▶	0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	1.1b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 t (fabs.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 2)))) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (.f64 v v))))
	42.0b	(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 (.f64 v v) 5)) 3) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) 3) (pow.f64 (-.f64 1 (*.f64 v v)) 3))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))

Compiler

Compiled 8315 to 5593 computations (32.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
✓	0.3b	(.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
✓	0.4b	(.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
✓	0.4b	(.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

series3.0s (28.4%)

Counts

4 → 96

Calls

4 calls:

1.2s	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
878.0ms	(.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
862.0ms	(.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
47.0ms	(.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

rewrite203.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`sqrt-div_binary64`
346×	`associate-*r/_binary64`
168×	`frac-times_binary64`
158×	`cbrt-div_binary64`
143×	`flip--_binary64`

Counts

4 → 239

Calls

4 calls:

30.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
20.0ms	(.f64 (.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
12.0ms	(.f64 (.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
6.0ms	(.f64 (.f64 (PI.f64) t) (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))

simplify383.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

628×	`associate-/l*_binary64`
278×	`*-commutative_binary64`
200×	`associate-l_binary64`
189×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

335 → 505

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	678	27374
1	2214	22657
2	5082	22657

prune1.3s (12.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	500	5	505
Fresh	4	1	5
Picked	1	0	1
Done	0	2	2
Total	505	8	513

Error

0.0b

Counts

513 → 8

Alt Table

Status	Error	Program
	29.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
✓	0.7b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 (PI.f64) (.f64 t (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
	1.4b	(/.f64 (cbrt.f64 1/2) (.f64 (PI.f64) (.f64 t (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 (-.f64 1 (.f64 3 (*.f64 v v))) 1/6)))))
	1.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 t (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 (-.f64 1 (.f64 3 (.f64 v v))) 1/6)))) (cbrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
✓	0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) (.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
	0.6b	(.f64 (cbrt.f64 (/.f64 1/2 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 (PI.f64) (.f64 t (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 (-.f64 1 (.f64 3 (.f64 v v))) 1/6)))) (-.f64 1 (.f64 v v)))))
	1.3b	(.f64 (/.f64 1 (.f64 (PI.f64) (.f64 t (fabs.f64 (.f64 (pow.f64 (sqrt.f64 2) 1/3) (pow.f64 (-.f64 1 (*.f64 3 (pow.f64 v 2))) 1/6)))))) (pow.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) 1/3))

Compiler

Compiled 45334 to 32108 computations (29.2% saved)

regimes1.4s (13.6%)

Accuracy

Total 0.3b remaining (78.8%)

Threshold costs 0.3b (78.8%)

Counts

176 → 1

Compiler

Compiled 45118 to 32351 computations (28.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	44
1	31	44
2	37	44
3	41	44
4	43	44
5	42	44

end1.0ms (0%)

Compiler: Compiled 31 to 22 computations (29% saved)

sample1.1s (10.7%)

Algorithm

1×

intervals

Results

703.0ms	8000×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 397 to 293 computations (26.2% saved)

Details

analyze177.0ms (1.7%)

sample31.0ms (0.3%)

simplify34.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series199.0ms (1.9%)

rewrite43.0ms (0.4%)

simplify136.0ms (1.3%)

prune273.0ms (2.6%)

localize17.0ms (0.2%)

series794.0ms (7.6%)

rewrite78.0ms (0.7%)

simplify156.0ms (1.5%)

prune552.0ms (5.3%)

localize15.0ms (0.1%)

series165.0ms (1.6%)

rewrite32.0ms (0.3%)

simplify108.0ms (1%)

prune259.0ms (2.5%)

localize20.0ms (0.2%)

series3.0s (28.4%)

rewrite203.0ms (1.9%)

simplify383.0ms (3.7%)

prune1.3s (12.1%)

regimes1.4s (13.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.1s (10.7%)

Profiling