Details

analyze3.0s (12%)

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)

sample5.2s (20.6%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.6s	6205×	body	128	valid
833.0ms	807×	body	1024	valid
797.0ms	485×	body	1024	invalid
752.0ms	809×	body	512	valid
592.0ms	2482×	body	128	invalid
270.0ms	396×	body	512	invalid
194.0ms	429×	body	256	valid
89.0ms	203×	body	256	invalid
11.0ms	6×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify118.0ms (0.5%)

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

3.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.3b	(.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)

localize12.0ms (0%)

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)))
✓	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.2s (12.5%)

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)))
1.1s	(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)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite17.0ms (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))

simplify430.0ms (1.7%)

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

prune1.3s (5.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	250	13	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	13	264

Error

3.0b

Counts

264 → 13

Alt Table

Status	Error	Program
	39.2b	(-.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))))))
	44.3b	(.f64 R (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) lambda1)))))) (.f64 lambda2 (.f64 phi1 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1)))) (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) lambda1)))))) (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) lambda1)))))) (.f64 phi1 phi2) (.f64 1/2 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) lambda1)))))) (.f64 phi1 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) (.f64 lambda1 lambda1))))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) lambda1)))))) (.f64 (.f64 lambda2 lambda2) (.f64 phi1 (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (*.f64 1/2 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))))
	15.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	36.3b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	9.1b	(.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 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	33.4b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	8.7b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
▶	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) lambda1))) (fma.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))))
	3.8b	(.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)))

Compiler

Compiled 60695 to 41524 computations (31.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
✓	0.4b	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series720.0ms (2.8%)

Counts

3 → 96

Calls

3 calls:

689.0ms

(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

25.0ms

(*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

6.0ms

(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms

(*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

0.0ms

(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

0.0ms

(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
625×	`cancel-sign-sub-inv_binary64`
254×	`fma-neg_binary64`
224×	`sub-neg_binary64`
204×	`associate-r_binary64`

Counts

142 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	3127
1	707	3007
2	2560	2947
3	5482	2947

prune330.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	156	13	169

Error

2.9b

Counts

169 → 13

Alt Table

Status	Error	Program
	12.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi1))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 1/8 (+.f64 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)) (+.f64 1 (cos.f64 (.f64 1/2 phi1)))) (.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)) phi2)))))))) (-.f64 phi1 phi2)))
	39.2b	(-.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))))))
	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))))
	8.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
▶	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	33.4b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	36.3b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	13.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (.f64 (.f64 phi1 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)) (pow.f64 (+.f64 1 (cos.f64 (.f64 1/2 phi2))) 2)) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))))) (-.f64 phi1 phi2)))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	3.8b	(.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)))
	14.7b	(.f64 R (hypot.f64 (fma.f64 1/2 (.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 lambda1 lambda2)) (.f64 1/2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1))))) (-.f64 phi1 phi2)))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) lambda1))) (fma.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))))

Compiler

Compiled 5979 to 3593 computations (39.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.4b	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series52.0ms (0.2%)

Counts

3 → 96

Calls

3 calls:

31.0ms

(*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

16.0ms

(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

6.0ms

(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms

(*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

0.0ms

(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

0.0ms

(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

891×	`cancel-sign-sub-inv_binary64`
691×	`fma-neg_binary64`
330×	`sub-neg_binary64`
306×	`associate-r_binary64`
253×	`neg-sub0_binary64`

Counts

142 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	246	3092
1	708	2973
2	2543	2812
3	4150	2798
4	5030	2798

prune344.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	156	13	169

Error

2.9b

Counts

169 → 13

Alt Table

Status	Error	Program
	12.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi1))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 1/8 (+.f64 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)) (+.f64 1 (cos.f64 (.f64 1/2 phi1)))) (.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)) phi2)))))))) (-.f64 phi1 phi2)))
	39.2b	(-.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))))))
▶	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))))
	8.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
✓	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	33.4b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	36.3b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	13.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (.f64 (.f64 phi1 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)) (pow.f64 (+.f64 1 (cos.f64 (.f64 1/2 phi2))) 2)) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))))) (-.f64 phi1 phi2)))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	14.7b	(.f64 R (hypot.f64 (fma.f64 1/2 (.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) lambda2) (fma.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 lambda1 lambda2) (.f64 (.f64 phi1 (.f64 (sin.f64 (*.f64 1/2 phi2)) lambda1)) -1/2))) (-.f64 phi1 phi2)))
	58.6b	(-.f64 (+.f64 (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) lambda1))) (fma.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))))
	3.8b	(.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)))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))

Compiler

Compiled 5814 to 3463 computations (40.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.2b	(.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
✓	0.4b	(.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))))
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series5.6s (22.1%)

Counts

2 → 88

Calls

2 calls:

3.6s

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

2.1s

(*.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))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

6.0ms

(*.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))))

5.0ms

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

simplify418.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

981×	`associate-r_binary64`
422×	`fma-def_binary64`
372×	`associate-+r+_binary64`
163×	`associate-l_binary64`
59×	`sqr-pow_binary64`

Counts

135 → 178

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1971	45762
1	5443	45762

prune1.5s (5.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	307	7	314
Fresh	4	7	11
Picked	1	0	1
Done	1	0	1
Total	313	14	327

Error

2.9b

Counts

327 → 14

Alt Table

Status	Error	Program
	12.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi1))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 1/8 (+.f64 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)) (+.f64 1 (cos.f64 (.f64 1/2 phi1)))) (.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (.f64 (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)) phi2)))))))) (-.f64 phi1 phi2)))
	3.7b	(.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) (.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))))
	33.4b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	53.7b	(.f64 (cbrt.f64 (.f64 (.f64 R (.f64 R R)) (.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)))))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	13.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (.f64 (.f64 phi1 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)) (pow.f64 (+.f64 1 (cos.f64 (.f64 1/2 phi2))) 2)) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))))) (-.f64 phi1 phi2)))
	3.9b	(.f64 (.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	36.3b	(exp.f64 (+.f64 (+.f64 (log.f64 R) (log.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (log.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	8.8b	(.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 1/2 phi2))) (-.f64 phi1 phi2))))
	9.3b	(.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 1/2 phi1))) (-.f64 phi1 phi2))))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))
	8.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	3.8b	(.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 (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))))
	14.7b	(.f64 R (hypot.f64 (fma.f64 1/2 (.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) lambda2) (fma.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 lambda1 lambda2) (.f64 (.f64 phi1 (.f64 (sin.f64 (*.f64 1/2 phi2)) lambda1)) -1/2))) (-.f64 phi1 phi2)))

Compiler

Compiled 66991 to 44906 computations (33% saved)

regimes2.5s (9.9%)

Accuracy

Total 0.4b remaining (10.1%)

Threshold costs 0.4b (10.1%)

Counts

190 → 1

Compiler

Compiled 65133 to 43859 computations (32.7% 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	17	28
1	24	28
2	32	28
3	36	28
4	38	28
5	38	28

end355.0ms (1.4%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 740 to 483 computations (34.7% saved)

Details

analyze3.0s (12%)

sample5.2s (20.6%)

simplify118.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0%)

series3.2s (12.5%)

rewrite17.0ms (0.1%)

simplify430.0ms (1.7%)

prune1.3s (5.1%)

localize15.0ms (0.1%)

series720.0ms (2.8%)

rewrite8.0ms (0%)

simplify86.0ms (0.3%)

prune330.0ms (1.3%)

localize16.0ms (0.1%)

series52.0ms (0.2%)

rewrite8.0ms (0%)

simplify105.0ms (0.4%)

prune344.0ms (1.4%)

localize14.0ms (0.1%)

series5.6s (22.1%)

rewrite15.0ms (0.1%)

simplify418.0ms (1.6%)

prune1.5s (5.8%)

regimes2.5s (9.9%)

simplify3.0ms (0%)

end355.0ms (1.4%)

Profiling