Details

analyze6.4s (21.1%)

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)

sample237.0ms (0.8%)

Algorithm

1×

intervals

Results

53.0ms	33×	body	1024	valid
47.0ms	190×	body	128	valid
25.0ms	18×	body	1024	invalid
18.0ms	77×	body	128	invalid
18.0ms	22×	body	512	valid
9.0ms	10×	body	512	invalid
6.0ms	11×	body	256	valid
2.0ms	4×	body	256	invalid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify129.0ms (0.4%)

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

prune8.0ms (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

4.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.3b	(.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)

localize24.0ms (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)))
✓	3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series6.0s (19.6%)

Counts

4 → 180

Calls

4 calls:

3.7s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
2.2s	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
45.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite31.0ms (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:

12.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
7.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))

simplify846.0ms (2.8%)

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

prune2.6s (8.4%)

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

4.1b

Counts

264 → 13

Alt Table

Status	Error	Program
	4.4b	(.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)))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	9.2b	(.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 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	18.0b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	14.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	42.7b	(-.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))))))
	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	4.7b	(.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) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	5.4b	(.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))))
	37.8b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))

Compiler

Compiled 60251 to 41216 computations (31.6% saved)

localize29.0ms (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)))
	3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.0s (3.4%)

Counts

3 → 96

Calls

3 calls:

969.0ms

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

54.0ms

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

10.0ms

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

rewrite15.0ms (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:

9.0ms

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

1.0ms

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

1.0ms

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

simplify165.0ms (0.5%)

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

prune591.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	155	14	169

Error

4.1b

Counts

169 → 14

Alt Table

Status	Error	Program
	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	4.7b	(.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) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	12.4b	(.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)))
	37.8b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	15.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	18.0b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	10.3b	(.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 (-.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)))
	4.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	42.7b	(-.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))))))
▶	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	5.4b	(.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))))

Compiler

Compiled 5997 to 3583 computations (40.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
✓	0.4b	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series83.0ms (0.3%)

Counts

3 → 96

Calls

3 calls:

45.0ms

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

29.0ms

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

9.0ms

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

rewrite16.0ms (0.1%)

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:

10.0ms

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

1.0ms

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

1.0ms

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

simplify185.0ms (0.6%)

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

prune594.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	156	14	170

Error

4.1b

Counts

170 → 14

Alt Table

Status	Error	Program
	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
▶	4.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)))) (-.f64 phi1 phi2)))
	4.7b	(.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) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	12.4b	(.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)))
	37.8b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	15.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	18.0b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	10.3b	(.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 (-.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)))
	4.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
✓	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	5.4b	(.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))))

Compiler

Compiled 5834 to 3459 computations (40.7% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))
✓	0.5b	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3))
✓	0.8b	(pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)
✓	3.4b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series269.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

200.0ms	(pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)
28.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3))
27.0ms	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))
9.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3))
3.0ms	(pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)
1.0ms	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))

simplify197.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

721×	`associate-r_binary64`
586×	`fma-def_binary64`
478×	`associate-l_binary64`
443×	`associate-+r+_binary64`
272×	`associate-+l+_binary64`

Counts

164 → 143

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	398	5875
1	1260	5547
2	5414	5547

prune725.0ms (2.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	142	15	157

Error

4.1b

Counts

157 → 15

Alt Table

Status	Error	Program
	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3) 3))))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (*.f64 1/2 phi2))) 3)))) (-.f64 phi1 phi2)))
	4.7b	(.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) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	12.4b	(.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)))
	37.8b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	15.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (.f64 1/2 (/.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (+.f64 1 (cos.f64 (*.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	18.0b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	4.4b	(.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)))
	4.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)) (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3))) (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) 3)))))) (-.f64 phi1 phi2)))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 (*.f64 1/2 phi1))) 3)))) (-.f64 phi1 phi2)))
✓	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	5.4b	(.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))))

Compiler

Compiled 8006 to 5579 computations (30.3% saved)

regimes2.7s (8.8%)

Accuracy

Total 0.3b remaining (7.1%)

Threshold costs 0.3b (7.1%)

Counts

137 → 1

Compiler

Compiled 35379 to 25013 computations (29.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-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	23	24
2	31	24
3	35	24
4	37	24
5	37	24

end49.0ms (0.2%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 105 to 70 computations (33.3% saved)

sample7.5s (24.6%)

Algorithm

1×

intervals

Results

1.9s	5933×	body	128	valid
1.2s	855×	body	1024	valid
776.0ms	807×	body	512	valid
667.0ms	445×	body	1024	invalid
665.0ms	2372×	body	128	invalid
313.0ms	372×	body	512	invalid
231.0ms	402×	body	256	valid
100.0ms	184×	body	256	invalid
8.0ms	3×	body	2048	valid

Compiler

Compiled 599 to 401 computations (33.1% saved)

Details

analyze6.4s (21.1%)

sample237.0ms (0.8%)

simplify129.0ms (0.4%)

prune8.0ms (0%)

localize24.0ms (0.1%)

series6.0s (19.6%)

rewrite31.0ms (0.1%)

simplify846.0ms (2.8%)

prune2.6s (8.4%)

localize29.0ms (0.1%)

series1.0s (3.4%)

rewrite15.0ms (0%)

simplify165.0ms (0.5%)

prune591.0ms (1.9%)

localize28.0ms (0.1%)

series83.0ms (0.3%)

rewrite16.0ms (0.1%)

simplify185.0ms (0.6%)

prune594.0ms (2%)

localize33.0ms (0.1%)

series269.0ms (0.9%)

rewrite18.0ms (0.1%)

simplify197.0ms (0.6%)

prune725.0ms (2.4%)

regimes2.7s (8.8%)

simplify5.0ms (0%)

end49.0ms (0.2%)

sample7.5s (24.6%)

Profiling