Details

analyze3.1s (8.4%)

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
3.1%	96.6%	0.2%	10
15.6%	84.2%	0.2%	11
15.6%	84.2%	0.2%	12
19.1%	80.7%	0.2%	13
25.7%	74%	0.2%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample3.1s (8.3%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.3s	6132×	body	128	valid
856.0ms	883×	body	1024	valid
587.0ms	825×	body	512	valid
185.0ms	412×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify153.0ms (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

prune7.0ms (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

2.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.7b	(.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)

localize17.0ms (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))
✓	0.0b	(.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)))
✓	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series6.5s (17.4%)

Counts

4 → 180

Calls

4 calls:

4.5s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.9s	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
44.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite28.0ms (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)))
6.0ms	(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))

simplify820.0ms (2.2%)

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

prune2.7s (7.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	252	11	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	253	11	264

Error

2.4b

Counts

264 → 11

Alt Table

Status	Error	Program
	45.7b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	18.4b	(.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)))
	6.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	39.8b	(-.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 phi2 2) (+.f64 (pow.f64 phi1 2) (.f64 (pow.f64 lambda2 2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2)))) R) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 phi2 2) (+.f64 (pow.f64 phi1 2) (.f64 (pow.f64 lambda2 2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2))))))
	34.0b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	12.1b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1)) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	5.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	5.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
▶	3.5b	(.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))))
	26.2b	(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)))))
	33.4b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 60231 to 41230 computations (31.5% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
✓	0.5b	(*.f64 (cbrt.f64 R) (cbrt.f64 R))
✓	0.6b	(cbrt.f64 R)
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.9s (10.5%)

Counts

3 → 84

Calls

3 calls:

3.8s	(.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
60.0ms	(cbrt.f64 R)
47.0ms	(*.f64 (cbrt.f64 R) (cbrt.f64 R))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`

Counts

3 → 79

Calls

3 calls:

7.0ms	(*.f64 (cbrt.f64 R) (cbrt.f64 R))
6.0ms	(.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.0ms	(cbrt.f64 R)

simplify669.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

801×	`*-commutative_binary64`
596×	`associate-r_binary64`
253×	`+-commutative_binary64`
247×	`fma-def_binary64`
206×	`associate-+r+_binary64`

Counts

163 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1291	24902
1	4549	24754
2	5005	24754

prune1.7s (4.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	251	4	255
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	255	11	266

Error

2.4b

Counts

266 → 11

Alt Table

Status	Error	Program
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 R)) (pow.f64 (sqrt.f64 (cbrt.f64 R)) 3)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	45.7b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	18.4b	(.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)))
	6.7b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2))))
	34.0b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	12.1b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1)) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
▶	5.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	31.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	6.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	33.3b	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 R)))) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	26.2b	(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)))))

Compiler

Compiled 36202 to 23096 computations (36.2% saved)

localize12.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
✓	0.1b	(.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))

series641.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

626.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
14.0ms	(.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

11.0ms	(.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1)))
5.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))

simplify253.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

673×	`associate-r_binary64`
640×	`associate-l_binary64`
482×	`fma-def_binary64`
220×	`times-frac_binary64`
218×	`associate-/l*_binary64`

Counts

140 → 168

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	469	7960
1	1604	7390
2	5613	7390

prune517.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	167	12	179

Error

2.3b

Counts

179 → 12

Alt Table

Status	Error	Program
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 R)) (pow.f64 (sqrt.f64 (cbrt.f64 R)) 3)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	45.7b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	18.4b	(.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)))
	6.7b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2))))
	12.1b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1)) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	31.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	8.8b	(*.f64 R (hypot.f64 (-.f64 lambda1 lambda2) (-.f64 phi1 phi2)))
▶	6.3b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	30.4b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))))
	33.3b	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 R)))) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	35.6b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1))) (-.f64 phi1 phi2)))))
	26.2b	(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)))))

Compiler

Compiled 9962 to 5845 computations (41.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 R (expm1.f64 (log1p.f64 (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)))
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
✓	5.9b	(expm1.f64 (log1p.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))

series5.3s (14.3%)

Counts

2 → 108

Calls

2 calls:

3.5s

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

1.9s

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 31

Calls

2 calls:

5.0ms

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

1.0ms

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

simplify791.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1109×	`associate-r_binary64`
439×	`fma-def_binary64`
146×	`associate-l_binary64`
73×	`sub-neg_binary64`
65×	`associate-/l*_binary64`

Counts

139 → 220

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2159	44146
1	5049	44146

prune3.0s (8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	286	2	288
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	287	13	300

Error

2.3b

Counts

300 → 13

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	31.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 R)) (pow.f64 (sqrt.f64 (cbrt.f64 R)) 3)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	45.7b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	18.4b	(.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)))
	6.7b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2))))
	12.1b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1)) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	8.8b	(*.f64 R (hypot.f64 (-.f64 lambda1 lambda2) (-.f64 phi1 phi2)))
	30.4b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))))
	33.3b	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 R)))) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	35.6b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi1))) (-.f64 phi1 phi2)))))
	26.2b	(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)))))
	9.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))))

Compiler

Compiled 60655 to 41460 computations (31.6% saved)

regimes3.4s (9.3%)

Accuracy

Total 0.2b remaining (8.5%)

Threshold costs 0.2b (8.5%)

Counts

164 → 1

Compiler

Compiled 37737 to 24743 computations (34.4% saved)

simplify6.0ms (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	17	24
1	27	24
2	34	24
3	38	24
4	40	24
5	39	24

end479.0ms (1.3%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 518 to 338 computations (34.7% saved)

Details

analyze3.1s (8.4%)

sample3.1s (8.3%)

simplify153.0ms (0.4%)

prune7.0ms (0%)

localize17.0ms (0%)

series6.5s (17.4%)

rewrite28.0ms (0.1%)

simplify820.0ms (2.2%)

prune2.7s (7.4%)

localize30.0ms (0.1%)

series3.9s (10.5%)

rewrite21.0ms (0.1%)

simplify669.0ms (1.8%)

prune1.7s (4.5%)

localize12.0ms (0%)

series641.0ms (1.7%)

rewrite21.0ms (0.1%)

simplify253.0ms (0.7%)

prune517.0ms (1.4%)

localize32.0ms (0.1%)

series5.3s (14.3%)

rewrite9.0ms (0%)

simplify791.0ms (2.1%)

prune3.0s (8%)

regimes3.4s (9.3%)

simplify6.0ms (0%)

end479.0ms (1.3%)

Profiling