Details

analyze3.0s (17.9%)

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
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample284.0ms (1.7%)

Algorithm

1×

intervals

Results

193.0ms	143×	body	1280	valid
59.0ms	79×	body	640	valid
12.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid
1.0ms	1×	body	640	invalid
1.0ms	3×	body	80	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	79	31
1	79	31

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 13.4b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `acos-asin_binary64` `cos-diff_binary64` `sin-mult_binary64` `cos-sum_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series413.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
76.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
74.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
35.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify128.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4964	1519
1	4964	1519

prune111.0ms (0.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	54	16	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	16	71

Merged error: 2.4b

Counts

71 → 16

Compiler

Compiled 2206 to 602 computations (72.7% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`sin-mult_binary64`
1×	`acos-asin_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series593.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
108.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
81.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
80.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify170.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5010	2055

prune135.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	67	13	80
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	78	18	96

Merged error: 2.3b

Counts

96 → 18

Compiler

Compiled 3224 to 760 computations (76.4% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
4.6b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
4×	`insert-posit16`
3×	`log-prod_binary64` `log-pow_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`acos-asin_binary64` `rem-log-exp_binary64` `sin-mult_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
3.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series566.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
88.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
82.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
73.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify171.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4931	2008
1	4931	2008

prune125.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	75	18	93

Merged error: 2.3b

Counts

93 → 18

Compiler

Compiled 3176 to 764 computations (75.9% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.1b	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.9b	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
4×	`insert-posit16`
3×	`log-prod_binary64` `log-pow_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`acos-asin_binary64` `rem-log-exp_binary64` `sin-mult_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
3.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))
3.0ms	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series563.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
98.0ms	(acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
77.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
75.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4934	2008
1	4934	2008

prune80.0ms (0.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	75	18	93

Merged error: 2.3b

Counts

93 → 18

Compiler

Compiled 2493 to 313 computations (87.4% saved)

regimes401.0ms (2.4%)

Compiler: Compiled 5051 to 3343 computations (33.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	47
1	33	47

end0.0ms (0%)

sample9.6s (57.4%)

Algorithm

1×

intervals

Results

6.3s	4704×	body	1280	valid
1.7s	2167×	body	640	valid
362.0ms	713×	body	320	valid
96.0ms	280×	body	160	valid
24.0ms	131×	body	80	valid
18.0ms	5×	body	2560	valid
6.0ms	4×	body	1280	invalid
1.0ms	1×	body	640	invalid

Compiler

Compiled 731 to 488 computations (33.2% saved)

Details

analyze3.0s (17.9%)

sample284.0ms (1.7%)

simplify26.0ms (0.2%)

prune3.0ms (0%)

localize28.0ms (0.2%)

rewrite19.0ms (0.1%)

series413.0ms (2.5%)

simplify128.0ms (0.8%)

prune111.0ms (0.7%)

localize31.0ms (0.2%)

rewrite20.0ms (0.1%)

series593.0ms (3.5%)

simplify170.0ms (1%)

prune135.0ms (0.8%)

localize37.0ms (0.2%)

rewrite16.0ms (0.1%)

series566.0ms (3.4%)

simplify171.0ms (1%)

prune125.0ms (0.7%)

localize34.0ms (0.2%)

rewrite18.0ms (0.1%)

series563.0ms (3.4%)

simplify160.0ms (1%)

prune80.0ms (0.5%)

regimes401.0ms (2.4%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample9.6s (57.4%)

Profiling