Details

analyze3.5s (14.1%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 29 to 18 computations (37.9% saved)

sample11.6s (46.6%)

Alt Table

Status	Error	Program
▶	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Results

9.0s	5466×	body	1024	valid
1.2s	1340×	body	512	valid
718.0ms	179×	body	2048	valid
257.0ms	838×	body	128	valid
250.0ms	433×	body	256	valid

Compiler

Compiled 142 to 87 computations (38.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	4.2b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.4b	(sin.f64 (-.f64 lambda1 lambda2))

series58.0ms (0.2%)

Counts

4 → 100

Calls

4 calls:

35.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
16.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite70.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

289×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
281×	`fma-neg_binary64`
158×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`

Counts

4 → 93

Calls

4 calls:

67.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
67.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
67.0ms	(cos.f64 (-.f64 lambda1 lambda2))
67.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	289	39
2	3912	39
3	5091	39
0	0	0
1	0	0

prune343.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	178	15	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	15	194

Error

5.5b

Counts

194 → 15

Alt Table

Status	Error	Program
	32.6b	(atan2.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.5b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (+.f64 (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (pow.f64 lambda2 2)))) (.f64 (cos.f64 phi2) (.f64 lambda2 (cos.f64 lambda1))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	31.9b	(atan2.f64 (.f64 (sin.f64 (neg.f64 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3))))
	12.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
	11.7b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	5.9b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	25.0b	(atan2.f64 (.f64 (-.f64 (+.f64 (.f64 (cos.f64 (neg.f64 lambda2)) lambda1) (sin.f64 (neg.f64 lambda2))) (+.f64 (.f64 1/2 (.f64 (sin.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))) (.f64 1/6 (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 3))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.7b	(atan2.f64 (.f64 (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	17.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	15.4b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 7070 to 1607 computations (77.3% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
✓	4.2b	(cos.f64 (-.f64 lambda1 lambda2))

series1.9s (7.7%)

Counts

4 → 80

Calls

4 calls:

960.0ms	(fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
622.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
337.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite78.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

364×	`fma-def_binary64`
268×	`expm1-udef_binary64`
268×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
160×	`add-sqr-sqrt_binary64`

Counts

4 → 110

Calls

4 calls:

75.0ms	(fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
75.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
75.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
75.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	314	43
2	3666	43
3	4941	43
0	0	0
1	0	0

prune491.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	290	13	303

Error

0.1b

Counts

303 → 13

Alt Table

Status	Error	Program
	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	0.4b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	12.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.8b	(atan2.f64 (.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) 1/3) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.7b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.5b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (+.f64 (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (pow.f64 lambda2 2)))) (.f64 (cos.f64 phi2) (.f64 lambda2 (cos.f64 lambda1))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.7b	(atan2.f64 (.f64 (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))
	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cos.f64 lambda1) (pow.f64 (cbrt.f64 (cos.f64 lambda2)) 2)) (cbrt.f64 (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
▶	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	15.4b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 15656 to 3100 computations (80.2% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
✓	0.4b	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
✓	0.7b	(cbrt.f64 (sin.f64 lambda1))

series1.2s (4.9%)

Counts

4 → 72

Calls

4 calls:

623.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
330.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
133.0ms	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
127.0ms	(cbrt.f64 (sin.f64 lambda1))

rewrite89.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
94×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

86.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
86.0ms	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
86.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
86.0ms	(cbrt.f64 (sin.f64 lambda1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	213	32
2	2148	32
3	5024	32
0	0	0
1	0	0

prune761.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	292	3	295
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	295	13	308

Error

0.0b

Counts

308 → 13

Alt Table

Status	Error	Program
▶	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (cos.f64 lambda2))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	2.3b	(atan2.f64 (.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) 1/3) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	0.4b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	12.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.5b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (+.f64 (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (pow.f64 lambda2 2)))) (.f64 (cos.f64 phi2) (.f64 lambda2 (cos.f64 lambda1))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.7b	(atan2.f64 (.f64 (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))
	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cos.f64 lambda1) (pow.f64 (cbrt.f64 (cos.f64 lambda2)) 2)) (cbrt.f64 (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	30.8b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (pow.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 1/3) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	11.7b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 20072 to 4482 computations (77.7% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
✓	0.4b	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
✓	0.7b	(cbrt.f64 (sin.f64 lambda1))

series1.4s (5.6%)

Counts

4 → 72

Calls

4 calls:

712.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
408.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
144.0ms	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
132.0ms	(cbrt.f64 (sin.f64 lambda1))

rewrite61.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
94×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

59.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))))
59.0ms	(pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2)
59.0ms	(cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
59.0ms	(cbrt.f64 (sin.f64 lambda1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	213	32
2	2148	32
3	5024	32
0	0	0
1	0	0

prune612.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	279	12	291

Error

0.0b

Counts

291 → 12

Alt Table

Status	Error	Program
	0.4b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	12.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	2.3b	(atan2.f64 (.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) 1/3) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	24.5b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (+.f64 (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (pow.f64 lambda2 2)))) (.f64 (cos.f64 phi2) (.f64 lambda2 (cos.f64 lambda1))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.7b	(atan2.f64 (.f64 (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))
	2.3b	(atan2.f64 (.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) 1/3) (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (cos.f64 lambda2))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 lambda1)) 2) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))
	0.3b	(atan2.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (.f64 (cos.f64 lambda1) (pow.f64 (cbrt.f64 (cos.f64 lambda2)) 2)) (cbrt.f64 (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	11.7b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 18482 to 3906 computations (78.9% saved)

regimes2.2s (8.9%)

Accuracy

Total 0.3b remaining (73.5%)

Threshold costs 0.3b (73.5%)

Counts

223 → 1

Compiler

Compiled 65616 to 37394 computations (43% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	92
1	55	92
2	77	92
3	92	92
4	102	92
5	105	92
6	105	92

end343.0ms (1.4%)

Compiler: Compiled 690 to 381 computations (44.8% saved)

Details

analyze3.5s (14.1%)

sample11.6s (46.6%)

localize20.0ms (0.1%)

series58.0ms (0.2%)

rewrite70.0ms (0.3%)

prune343.0ms (1.4%)

localize29.0ms (0.1%)

series1.9s (7.7%)

rewrite78.0ms (0.3%)

prune491.0ms (2%)

localize34.0ms (0.1%)

series1.2s (4.9%)

rewrite89.0ms (0.4%)

prune761.0ms (3.1%)

localize39.0ms (0.2%)

series1.4s (5.6%)

rewrite61.0ms (0.2%)

prune612.0ms (2.5%)

regimes2.2s (8.9%)

simplify5.0ms (0%)

end343.0ms (1.4%)

Profiling