Details

analyze2.8s (13.9%)

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)

sample4.7s (23.2%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.7s	6201×	body	128	valid
786.0ms	827×	body	1024	valid
624.0ms	787×	body	512	valid
530.0ms	2411×	body	128	invalid
441.0ms	429×	body	1024	invalid
246.0ms	398×	body	512	invalid
182.0ms	430×	body	256	valid
79.0ms	197×	body	256	invalid
20.0ms	11×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify119.0ms (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

3.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.8b	(.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)))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.1s (15.4%)

Counts

4 → 180

Calls

4 calls:

2.1s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.0s	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
24.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite16.0ms (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))

simplify424.0ms (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 (5.7%)

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

3.3b

Counts

264 → 13

Alt Table

Status	Error	Program
	30.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3)))) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2) (.f64 1/8 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)))))) (-.f64 phi1 phi2)))
	4.9b	(.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))))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	40.6b	(.f64 R (hypot.f64 (.f64 (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	27.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.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)))
	9.0b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.2b	(.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))))
	35.5b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	47.9b	(.f64 (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))))) R)
	38.2b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	11.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	16.3b	(.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)))

Compiler

Compiled 60267 to 41262 computations (31.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
✓	0.4b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.1s (5.5%)

Counts

3 → 72

Calls

3 calls:

622.0ms

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

494.0ms

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

6.0ms

(*.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))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.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))))

6.0ms

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

1.0ms

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

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

593×	`cancel-sign-sub-inv_binary64`
348×	`fma-neg_binary64`
345×	`neg-mul-1_binary64`
308×	`distribute-rgt-neg-in_binary64`
298×	`unswap-sqr_binary64`

Counts

165 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3909
1	655	3651
2	2239	3332
3	4444	3263
4	4993	3263

prune762.0ms (3.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	328	6	334
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	331	16	347

Error

3.3b

Counts

347 → 16

Alt Table

Status	Error	Program
	9.0b	(.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) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	30.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (fma.f64 (sin.f64 (.f64 1/2 phi1)) (-.f64 (.f64 1/48 (pow.f64 phi2 3)) (.f64 1/2 phi2)) (.f64 (.f64 phi2 phi2) (.f64 (cos.f64 (.f64 1/2 phi1)) -1/8))))) (-.f64 phi1 phi2)))
	38.2b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
▶	3.8b	(.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)))
	11.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	40.6b	(.f64 R (hypot.f64 (.f64 (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	11.0b	(.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 1/2 phi1))))) (-.f64 phi1 phi2)))
	4.2b	(.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))))
	35.5b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.9b	(.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))))
	11.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	47.9b	(.f64 (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))))) R)
	16.3b	(.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)))

Compiler

Compiled 16099 to 9954 computations (38.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
✓	3.9b	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

series20.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

15.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
5.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow-unpow_binary64`
3×	`unpow-prod-down_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
2.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-r_binary64`
436×	`associate-l_binary64`
368×	`fma-def_binary64`
322×	`distribute-rgt-neg-in_binary64`
320×	`cancel-sign-sub-inv_binary64`

Counts

47 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1102
1	305	1033
2	894	990
3	3277	952
4	5026	952

prune344.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	146	13	159

Error

3.3b

Counts

159 → 13

Alt Table

Status	Error	Program
	11.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	10.9b	(.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 1/2 phi1))))) (-.f64 phi1 phi2)))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	40.6b	(.f64 R (hypot.f64 (.f64 (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
▶	3.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	30.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (fma.f64 (sin.f64 (.f64 1/2 phi1)) (-.f64 (.f64 1/48 (pow.f64 phi2 3)) (.f64 1/2 phi2)) (.f64 (.f64 phi2 phi2) (.f64 (cos.f64 (.f64 1/2 phi1)) -1/8))))) (-.f64 phi1 phi2)))
	4.2b	(.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))))
	35.5b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.9b	(.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))))
	11.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	47.9b	(.f64 (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))))) R)
	16.3b	(.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)))

Compiler

Compiled 6732 to 4323 computations (35.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.4b	(pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2)
	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.5s (7.2%)

Counts

2 → 48

Calls

2 calls:

1.4s

(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 phi1 1/2)) (cos.f64 (*.f64 phi2 1/2))) (*.f64 (sin.f64 (*.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

34.0ms

(pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 phi1 1/2)) (cos.f64 (*.f64 phi2 1/2))) (*.f64 (sin.f64 (*.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2)

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
12×	`associate-l_binary64`
12×	`unswap-sqr_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 68

Calls

2 calls:

12.0ms

(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 phi1 1/2)) (cos.f64 (*.f64 phi2 1/2))) (*.f64 (sin.f64 (*.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

6.0ms

(pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 phi1 1/2)) (cos.f64 (*.f64 phi2 1/2))) (*.f64 (sin.f64 (*.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2)

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
390×	`fma-def_binary64`
384×	`*-commutative_binary64`
324×	`cancel-sign-sub-inv_binary64`
321×	`distribute-rgt-in_binary64`

Counts

116 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	5661
1	443	5466
2	1258	5414
3	2958	5369
4	4948	5369

prune639.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	193	8	201
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	200	14	214

Error

3.2b

Counts

214 → 14

Alt Table

Status	Error	Program
	8.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3)) (cbrt.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3))) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi1))) (.f64 (sin.f64 (.f64 1/2 phi2)) (sin.f64 (*.f64 1/2 phi1)))) 2)))))) (-.f64 phi1 phi2)))
	16.3b	(.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)))
	10.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	4.2b	(.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))))
	10.9b	(.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 1/2 phi1))))) (-.f64 phi1 phi2)))
	8.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))))) (-.f64 phi1 phi2)))
	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (cbrt.f64 (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	35.5b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.9b	(.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))))
	40.6b	(.f64 R (hypot.f64 (.f64 (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sqrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	30.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (fma.f64 (sin.f64 (.f64 1/2 phi1)) (fma.f64 (pow.f64 phi2 3) 1/48 (.f64 phi2 -1/2)) (.f64 phi2 (.f64 phi2 (.f64 (cos.f64 (*.f64 1/2 phi1)) -1/8)))))) (-.f64 phi1 phi2)))
	23.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))) 2) 1/3) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 1/3))) (-.f64 phi1 phi2)))

Compiler

Compiled 11882 to 8379 computations (29.5% saved)

regimes2.7s (13.1%)

Accuracy

Total 0.3b remaining (9%)

Threshold costs 0.3b (9%)

Counts

207 → 1

Compiler

Compiled 73143 to 53642 computations (26.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	47	64
2	63	64
3	73	64
4	79	64
5	80	64
6	80	64

end460.0ms (2.3%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 933 to 694 computations (25.6% saved)

Details

analyze2.8s (13.9%)

sample4.7s (23.2%)

simplify119.0ms (0.6%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series3.1s (15.4%)

rewrite16.0ms (0.1%)

simplify424.0ms (2.1%)

prune1.2s (5.7%)

localize15.0ms (0.1%)

series1.1s (5.5%)

rewrite20.0ms (0.1%)

simplify118.0ms (0.6%)

prune762.0ms (3.7%)

localize20.0ms (0.1%)

series20.0ms (0.1%)

rewrite5.0ms (0%)

simplify60.0ms (0.3%)

prune344.0ms (1.7%)

localize28.0ms (0.1%)

series1.5s (7.2%)

rewrite31.0ms (0.2%)

simplify139.0ms (0.7%)

prune639.0ms (3.1%)

regimes2.7s (13.1%)

simplify4.0ms (0%)

end460.0ms (2.3%)

Profiling