Details

analyze3.5s (17.4%)

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)

sample153.0ms (0.8%)

Algorithm

1×

intervals

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

29.0ms	207×	body	128	valid
15.0ms	20×	body	1024	valid
14.0ms	17×	body	1024	invalid
10.0ms	77×	body	128	invalid
9.0ms	21×	body	512	valid
7.0ms	16×	body	512	invalid
2.0ms	8×	body	256	valid
1.0ms	4×	body	256	invalid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify118.0ms (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

3.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.1b	(.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)

localize13.0ms (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)))
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.0s (14.7%)

Counts

4 → 180

Calls

4 calls:

2.0s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
961.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
23.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite18.0ms (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:

9.0ms	(*.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))

simplify400.0ms (2%)

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 (5.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	247	16	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	248	16	264

Error

2.9b

Counts

264 → 16

Alt Table

Status	Error	Program
	27.8b	(.f64 R (hypot.f64 (cbrt.f64 (.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (-.f64 lambda1 lambda2)) (.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)))
	32.2b	(.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)))
	3.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	24.4b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))) (fma.f64 1/8 (.f64 lambda2 (.f64 (.f64 phi1 phi1) (cos.f64 (.f64 1/2 phi2)))) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1))) (fma.f64 1/2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1)) (fma.f64 1/8 (.f64 (.f64 phi1 phi1) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1)) (.f64 lambda2 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	4.3b	(.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))))
▶	3.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	42.6b	(-.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))))))
	36.1b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	3.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.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)))
	6.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	8.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.3b	(.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))))
	3.2b	(.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)))
	28.5b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 60661 to 41490 computations (31.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
✓	0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.8s (9%)

Counts

3 → 132

Calls

3 calls:

1.8s

(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))

23.0ms

(*.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

5.0ms

(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`log-prod_binary64`

Counts

3 → 71

Calls

3 calls:

9.0ms

(*.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

4.0ms

(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

3.0ms

(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))

simplify339.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

877×	`*-commutative_binary64`
674×	`associate-r_binary64`
279×	`+-commutative_binary64`
255×	`fma-def_binary64`
228×	`times-frac_binary64`

Counts

203 → 248

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1422	25780
1	4749	25607
2	5140	25607

prune897.0ms (4.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	266	5	271
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	270	17	287

Error

2.9b

Counts

287 → 17

Alt Table

Status	Error	Program
	32.2b	(.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)))
	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
▶	3.2b	(.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)))
	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	12.5b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) lambda2) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1)) (fma.f64 1/2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi2)) lambda2))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	42.6b	(-.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))))))
	36.1b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	28.5b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	3.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.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)))
	8.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	3.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.3b	(.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))))
✓	3.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	25.9b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))

Compiler

Compiled 35411 to 23495 computations (33.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.4b	(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))))
	3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series46.0ms (0.2%)

Counts

3 → 72

Calls

3 calls:

28.0ms

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

12.0ms

(*.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))))

rewrite16.0ms (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)))

simplify104.0ms (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

prune611.0ms (3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	5	10	15
Picked	1	0	1
Done	1	0	1
Total	216	18	234

Error

2.8b

Counts

234 → 18

Alt Table

Status	Error	Program
	8.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	24.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (-.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 (.f64 (.f64 (pow.f64 phi1 3) 1/6) (sin.f64 (.f64 1/2 phi2))) (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (.f64 phi1 phi1) 1/4) (-.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 (sin.f64 (.f64 1/2 phi2))))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	4.3b	(.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))))
▶	3.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	42.6b	(-.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))))))
	36.1b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	12.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) -1/2 (cos.f64 (*.f64 1/2 phi2)))) (-.f64 phi1 phi2)))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	28.5b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	26.7b	(.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)))
	7.6b	(.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 phi1))))) (-.f64 phi1 phi2)))
	3.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (/.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (+.f64 (cos.f64 (.f64 1 (+.f64 phi2 phi1))) 1))) (cbrt.f64 2))) (-.f64 phi1 phi2)))
	6.1b	(.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)))
	25.9b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))

Compiler

Compiled 9741 to 5738 computations (41.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	3.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.1s (5.4%)

Counts

2 → 48

Calls

2 calls:

617.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
476.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 25

Calls

2 calls:

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

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
441×	`cancel-sign-sub-inv_binary64`
318×	`neg-sub0_binary64`
318×	`neg-mul-1_binary64`
266×	`unswap-sqr_binary64`

Counts

73 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	1997
1	527	1983
2	1798	1847
3	4554	1847
4	5123	1847

prune603.0ms (3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	207	18	225

Error

2.8b

Counts

225 → 18

Alt Table

Status	Error	Program
	33.2b	(.f64 (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 (sqrt.f64 R) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	42.6b	(-.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) (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	25.9b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	36.1b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	12.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) -1/2 (cos.f64 (*.f64 1/2 phi2)))) (-.f64 phi1 phi2)))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	26.7b	(.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)))
	7.6b	(.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 phi1))))) (-.f64 phi1 phi2)))
	24.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 (.f64 (.f64 (pow.f64 phi1 3) 1/6) (sin.f64 (.f64 1/2 phi2))) (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (.f64 phi1 phi1) 1/4) (-.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	8.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	3.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.3b	(.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))))
	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (/.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (+.f64 (cos.f64 (.f64 1 (+.f64 phi2 phi1))) 1))) (cbrt.f64 2))) (-.f64 phi1 phi2)))
	6.1b	(.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)))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 9963 to 6106 computations (38.7% saved)

regimes2.1s (10.2%)

Accuracy

Total 0.2b remaining (5.9%)

Threshold costs 0.2b (5.9%)

Counts

175 → 1

Compiler

Compiled 52875 to 36776 computations (30.4% 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

end20.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 105 to 70 computations (33.3% saved)

sample4.1s (20.2%)

Algorithm

1×

intervals

Results

922.0ms	6097×	body	128	valid
590.0ms	750×	body	1024	valid
390.0ms	754×	body	512	valid
365.0ms	478×	body	1024	invalid
343.0ms	155×	body	256	invalid
333.0ms	2368×	body	128	invalid
162.0ms	364×	body	512	invalid
119.0ms	394×	body	256	valid
8.0ms	5×	body	2048	valid

Compiler

Compiled 696 to 469 computations (32.6% saved)

Details

analyze3.5s (17.4%)

sample153.0ms (0.8%)

simplify118.0ms (0.6%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series3.0s (14.7%)

rewrite18.0ms (0.1%)

simplify400.0ms (2%)

prune1.2s (5.8%)

localize15.0ms (0.1%)

series1.8s (9%)

rewrite19.0ms (0.1%)

simplify339.0ms (1.7%)

prune897.0ms (4.4%)

localize16.0ms (0.1%)

series46.0ms (0.2%)

rewrite16.0ms (0.1%)

simplify104.0ms (0.5%)

prune611.0ms (3%)

localize16.0ms (0.1%)

series1.1s (5.4%)

rewrite3.0ms (0%)

simplify78.0ms (0.4%)

prune603.0ms (3%)

regimes2.1s (10.2%)

simplify3.0ms (0%)

end20.0ms (0.1%)

sample4.1s (20.2%)

Profiling