Details

analyze3.4s (18%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample222.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

85.0ms	23×	body	1024	valid
24.0ms	193×	body	128	valid
12.0ms	31×	body	512	valid
12.0ms	16×	body	1024	invalid
9.0ms	75×	body	128	invalid
7.0ms	18×	body	512	invalid
2.0ms	9×	body	256	valid
2.0ms	9×	body	256	invalid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1413×	`unsub-neg_binary64`
897×	`distribute-neg-out_binary64`
703×	`fma-def_binary64`
583×	`neg-sub0_binary64`
478×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	35	24
2	83	24
3	224	24
4	658	24
5	2038	24
6	3128	24
7	3593	24
8	4399	24
9	4364	24
10	4430	24
11	4468	24
12	5035	24

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

3.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

Compiler

Compiled 95 to 55 computations (42.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.9s (15.1%)

Counts

4 → 180

Calls

4 calls:

1.8s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
984.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
22.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`associate-l_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 63

Calls

4 calls:

7.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
0.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))

simplify389.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1141×	`associate-r_binary64`
462×	`fma-def_binary64`
151×	`associate-l_binary64`
88×	`sub-neg_binary64`
65×	`associate-/l*_binary64`

Counts

243 → 263

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2275	46358
1	5160	46358

prune1.2s (6.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	248	15	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	15	264

Error

3.5b

Counts

264 → 15

Alt Table

Status	Error	Program
	9.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
▶	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	34.9b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	10.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	40.2b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	55.3b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	40.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	27.0b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/8 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 lambda2 (.f64 phi2 phi2))) (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (fma.f64 (cos.f64 (.f64 1/2 phi1)) lambda1 (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (pow.f64 phi2 3) lambda1)))))) (fma.f64 1/48 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3))) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (fma.f64 (cos.f64 (.f64 1/2 phi1)) lambda2 (.f64 1/8 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (*.f64 phi2 phi2) lambda1))))))) (-.f64 phi1 phi2)))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	5.1b	(.f64 (.f64 R (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	5.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	23.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (*.f64 1/2 phi2))))))) (-.f64 phi1 phi2)))
	27.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 60553 to 41424 computations (31.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series47.0ms (0.3%)

Counts

3 → 72

Calls

3 calls:

27.0ms

(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

14.0ms

(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms

(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

3.0ms

(cbrt.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

3.0ms

(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
860×	`fma-neg_binary64`
664×	`cancel-sign-sub-inv_binary64`
258×	`associate-r_binary64`
234×	`distribute-rgt-neg-in_binary64`

Counts

146 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	3575
1	534	2723
2	1856	2456
3	4257	2412
4	4983	2412

prune533.0ms (2.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	214	18	232

Error

3.5b

Counts

232 → 18

Alt Table

Status	Error	Program
	7.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	9.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
▶	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))
	22.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (-.f64 (+.f64 (.f64 3/4 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 phi2 2)))) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3)) (+.f64 (.f64 3/2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (.f64 3/8 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3) (pow.f64 phi2 2))))))) (-.f64 phi1 phi2)))
	23.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (*.f64 1/2 phi2))))))) (-.f64 phi1 phi2)))
	10.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	40.2b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	55.3b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	22.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (fma.f64 (.f64 phi2 phi2) (.f64 1/4 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2)) (fma.f64 (cos.f64 (.f64 1/2 phi1)) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 (sin.f64 (.f64 1/2 phi1)))) (.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) -1/4)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	40.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	5.1b	(.f64 (.f64 R (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	34.9b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	5.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	27.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 9767 to 5754 computations (41.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))
✓	0.5b	(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
✓	0.8b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6)
✓	3.0b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series1.1s (5.6%)

Counts

4 → 96

Calls

4 calls:

532.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))
516.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6)
7.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
5.0ms	(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.0ms	(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
2.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6)
1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
534×	`cancel-sign-sub-inv_binary64`
381×	`fma-neg_binary64`
246×	`distribute-rgt-neg-in_binary64`
242×	`unswap-sqr_binary64`

Counts

152 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	3049
1	576	2921
2	1918	2717
3	4492	2705
4	4948	2705

prune476.0ms (2.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	165	18	183

Error

3.4b

Counts

183 → 18

Alt Table

Status	Error	Program
	9.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
▶	4.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))))) (-.f64 phi1 phi2)))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	5.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	22.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (-.f64 (+.f64 (.f64 3/4 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 phi2 2)))) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3)) (+.f64 (.f64 3/2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (.f64 3/8 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3) (pow.f64 phi2 2))))))) (-.f64 phi1 phi2)))
	23.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (*.f64 1/2 phi2))))))) (-.f64 phi1 phi2)))
	18.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2) -1/2 (cos.f64 (.f64 1/2 phi1)))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))
	10.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	40.2b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	55.3b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	40.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	5.1b	(.f64 (.f64 R (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	34.9b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	27.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 7749 to 4863 computations (37.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))
	0.5b	(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
	0.8b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6)
	3.0b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series478.0ms (2.5%)

Counts

1 → 24

Calls

1 calls:

478.0ms

(cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`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 → 14

Calls

1 calls:

1.0ms

(cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

608×	`unswap-sqr_binary64`
519×	`fma-neg_binary64`
516×	`fma-def_binary64`
369×	`*-commutative_binary64`
265×	`sub-neg_binary64`

Counts

38 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1296
1	338	1284
2	1098	1013
3	3156	928
4	5024	928

prune1.9s (10.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	501	3	504
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	503	19	522

Error

3.4b

Counts

522 → 19

Alt Table

Status	Error	Program
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))))))) (-.f64 phi1 phi2)))
	34.9b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	22.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (-.f64 (+.f64 (.f64 3/4 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 phi2 2)))) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3)) (+.f64 (.f64 3/2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (.f64 3/8 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 3) (pow.f64 phi2 2))))))) (-.f64 phi1 phi2)))
	23.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (*.f64 1/2 phi2))))))) (-.f64 phi1 phi2)))
	18.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2) -1/2 (cos.f64 (.f64 1/2 phi1)))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))
	24.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (cbrt.f64 (cbrt.f64 (.f64 (+.f64 (+.f64 (fma.f64 1/4 (.f64 (.f64 phi2 phi2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2)) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2)) (.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi1))) (-.f64 (.f64 (pow.f64 phi2 3) 1/6) phi2))) (.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) -1/4))) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))))) (-.f64 phi1 phi2)))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 6) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (cbrt.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	10.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	40.2b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	55.3b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	40.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	9.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	5.1b	(.f64 (.f64 R (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	5.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	27.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 39512 to 25823 computations (34.6% saved)

regimes2.1s (11.2%)

Accuracy

Total 0.3b remaining (9.1%)

Threshold costs 0.3b (9.1%)

Counts

166 → 1

Compiler

Compiled 57006 to 39773 computations (30.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	22	24
2	30	24
3	34	24
4	36	24
5	36	24

end23.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 105 to 70 computations (33.3% saved)

sample3.6s (19.3%)

Algorithm

1×

intervals

Results

817.0ms	6116×	body	128	valid
564.0ms	763×	body	1024	valid
324.0ms	2420×	body	128	invalid
317.0ms	446×	body	1024	invalid
309.0ms	735×	body	512	valid
162.0ms	403×	body	512	invalid
114.0ms	378×	body	256	valid
42.0ms	155×	body	256	invalid
11.0ms	8×	body	2048	valid

Compiler

Compiled 889 to 605 computations (31.9% saved)

Details

analyze3.4s (18%)

sample222.0ms (1.2%)

simplify122.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series2.9s (15.1%)

rewrite15.0ms (0.1%)

simplify389.0ms (2.1%)

prune1.2s (6.5%)

localize16.0ms (0.1%)

series47.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify96.0ms (0.5%)

prune533.0ms (2.8%)

localize16.0ms (0.1%)

series1.1s (5.6%)

rewrite10.0ms (0.1%)

simplify101.0ms (0.5%)

prune476.0ms (2.5%)

localize22.0ms (0.1%)

series478.0ms (2.5%)

rewrite2.0ms (0%)

simplify58.0ms (0.3%)

prune1.9s (10.2%)

regimes2.1s (11.2%)

simplify3.0ms (0%)

end23.0ms (0.1%)

sample3.6s (19.3%)

Profiling