Details

analyze10.7s (24.2%)

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%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0.6%	99.2%	0.2%	13
1.8%	98%	0.2%	14

Compiler

Compiled 71 to 47 computations (33.8% saved)

sample680.0ms (1.5%)

Algorithm

1×

intervals

Results

460.0ms	165×	body	1024	valid
85.0ms	39×	body	512	valid
73.0ms	13×	body	2048	valid
14.0ms	15×	body	256	valid
10.0ms	24×	body	128	valid

Compiler

Compiled 146 to 98 computations (32.9% saved)

simplify167.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

714×	`distribute-rgt-neg-in_binary64`
578×	`sub-neg_binary64`
479×	`fabs-mul_binary64`
468×	`cube-prod_binary64`
458×	`sqr-pow_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	103
1	59	103
2	119	103
3	235	103
4	459	103
5	811	103
6	1302	103
7	2017	103
8	2988	103
9	3479	103
10	4058	103
11	4322	103
12	4127	103
13	3850	103
14	4705	103
15	4800	103

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

23.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Status

Error

Program

▶

23.4b

(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Compiler

Compiled 210 to 138 computations (34.3% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite149.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

23.2b

Rules

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

Counts

4 → 32

Calls

4 calls:

5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 2333 to 1346 computations (42.3% saved)

series201.0ms (0.5%)

Error

22.8b

Counts

4 → 40

Calls

4 calls:

31.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
30.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
27.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
26.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 6813 to 4435 computations (34.9% saved)

simplify94.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

585×	`distribute-rgt-neg-in_binary64`
566×	`cancel-sign-sub-inv_binary64`
442×	`distribute-lft-neg-in_binary64`
420×	`unsub-neg_binary64`
418×	`sub-neg_binary64`

Counts

72 → 20

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1268
1	147	1192
2	356	1150
3	959	1120
4	2106	1120
5	4300	1120
6	4998	1120

prune85.0ms (0.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	11	9	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	12	9	21

Error

22.9b

Counts

21 → 9

Alt Table

Status	Error	Program
	35.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	37.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (sin.f64 (.f64 lambda2 1/2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	38.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8))) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (+.f64 (.f64 1/2 lambda1) (.f64 (pow.f64 lambda1 3) -1/48))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
▶	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Compiler

Compiled 2971 to 1912 computations (35.6% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
8.5b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

rewrite178.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

22.9b

Rules

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

Counts

4 → 45

Calls

4 calls:

5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 3223 to 1914 computations (40.6% saved)

series226.0ms (0.5%)

Error

22.7b

Counts

4 → 40

Calls

4 calls:

36.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
35.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
31.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
25.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

Compiler

Compiled 7029 to 4651 computations (33.8% saved)

simplify152.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

585×	`distribute-rgt-neg-in_binary64`
566×	`cancel-sign-sub-inv_binary64`
528×	`unswap-sqr_binary64`
442×	`distribute-lft-neg-in_binary64`
387×	`*-commutative_binary64`

Counts

85 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	1439
1	183	1385
2	464	1343
3	1236	1313
4	2619	1295
5	4527	1295
6	4824	1295
7	4938	1295
8	4909	1295

prune119.0ms (0.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	30	5	35
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	32	12	44

Error

22.9b

Counts

44 → 12

Alt Table

Status	Error	Program
▶	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	35.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	37.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (sin.f64 (.f64 lambda2 1/2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	38.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8))) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (+.f64 (.f64 1/2 lambda1) (.f64 (pow.f64 lambda1 3) -1/48))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Compiler

Compiled 3875 to 2497 computations (35.6% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
8.5b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
8.5b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))

rewrite336.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

22.9b

Rules

72×	`cbrt-prod_binary64`
24×	`cube-prod_binary64`
24×	`unpow-prod-down_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 82

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))
5.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 4933 to 3037 computations (38.4% saved)

series244.0ms (0.6%)

Error

22.8b

Counts

4 → 40

Calls

4 calls:

42.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
38.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
27.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
27.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))

Compiler

Compiled 7185 to 4807 computations (33.1% saved)

simplify186.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

585×	`distribute-rgt-neg-in_binary64`
566×	`cancel-sign-sub-inv_binary64`
443×	`*-commutative_binary64`
442×	`distribute-lft-neg-in_binary64`
424×	`sub-neg_binary64`

Counts

122 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	2260
1	199	2116
2	502	2074
3	1344	2044
4	2739	1996
5	4311	1996
6	4870	1996
7	4990	1996
8	4903	1996

prune144.0ms (0.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Error

22.9b

Counts

86 → 12

Alt Table

Status	Error	Program
✓	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	35.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	37.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (sin.f64 (.f64 lambda2 1/2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	38.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8))) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (+.f64 (.f64 1/2 lambda1) (.f64 (pow.f64 lambda1 3) -1/48))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
▶	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Compiler

Compiled 4207 to 2700 computations (35.8% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
8.5b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

rewrite204.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

22.9b

Rules

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

Counts

4 → 45

Calls

4 calls:

6.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 3223 to 1914 computations (40.6% saved)

series246.0ms (0.6%)

Error

22.7b

Counts

4 → 40

Calls

4 calls:

32.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
32.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
30.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
26.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

Compiler

Compiled 7029 to 4651 computations (33.8% saved)

simplify150.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

585×	`distribute-rgt-neg-in_binary64`
566×	`cancel-sign-sub-inv_binary64`
528×	`unswap-sqr_binary64`
442×	`distribute-lft-neg-in_binary64`
387×	`*-commutative_binary64`

Counts

85 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	1439
1	183	1385
2	464	1343
3	1236	1313
4	2619	1295
5	4527	1295
6	4824	1295
7	4938	1295
8	4909	1295

prune115.0ms (0.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	35	12	47

Error

22.9b

Counts

47 → 12

Alt Table

Status	Error	Program
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	35.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	37.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (sin.f64 (.f64 lambda2 1/2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	38.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8))) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (+.f64 (.f64 1/2 lambda1) (.f64 (pow.f64 lambda1 3) -1/48))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	24.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (sin.f64 (/.f64 lambda1 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	23.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))

Compiler

Compiled 2894 to 1823 computations (37% saved)

regimes5.9s (13.3%)

Accuracy

Total 0.6b remaining (2.3%)

Threshold costs 0.6b (2.3%)

Compiler

Compiled 181984 to 124000 computations (31.9% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	103
1	52	103
2	69	103
3	89	103
4	107	103
5	123	103
6	133	103
7	139	103
8	141	103
9	140	103

end28.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 350 to 235 computations (32.9% saved)

sample23.8s (53.7%)

Algorithm

1×

intervals

Results

16.8s	5235×	body	1024	valid
2.6s	436×	body	2048	valid
2.2s	1275×	body	512	valid
451.0ms	376×	body	256	valid
378.0ms	678×	body	128	valid
5.0ms	2×	body	1024	invalid

Compiler

Compiled 1133 to 779 computations (31.2% saved)

Iter	Nodes	Cost
0	33	103
1	52	103
2	69	103
3	89	103
4	107	103
5	123	103
6	133	103
7	139	103
8	141	103
9	140	103

Iter	Nodes	Cost
0	33	103
1	52	103
2	69	103
3	89	103
4	107	103
5	123	103
6	133	103
7	139	103
8	141	103
9	140	103

Details

analyze10.7s (24.2%)

sample680.0ms (1.5%)

simplify167.0ms (0.4%)

prune5.0ms (0%)

localize35.0ms (0.1%)

rewrite149.0ms (0.3%)

series201.0ms (0.5%)

simplify94.0ms (0.2%)

prune85.0ms (0.2%)

localize45.0ms (0.1%)

rewrite178.0ms (0.4%)

series226.0ms (0.5%)

simplify152.0ms (0.3%)

prune119.0ms (0.3%)

localize43.0ms (0.1%)

rewrite336.0ms (0.8%)

series244.0ms (0.6%)

simplify186.0ms (0.4%)

prune144.0ms (0.3%)

localize43.0ms (0.1%)

rewrite204.0ms (0.5%)

series246.0ms (0.6%)

simplify150.0ms (0.3%)

prune115.0ms (0.3%)

regimes5.9s (13.3%)

simplify9.0ms (0%)

end28.0ms (0.1%)

sample23.8s (53.7%)

Profiling

Iter	Nodes	Cost
0	33	103
1	52	103
2	69	103
3	89	103
4	107	103
5	123	103
6	133	103
7	139	103
8	141	103
9	140	103