Details

analyze2.8s (16.9%)

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)

sample258.0ms (1.6%)

Algorithm

1×

intervals

Results

181.0ms	180×	body	1024	valid
31.0ms	45×	body	512	valid
23.0ms	9×	body	2048	valid
6.0ms	16×	body	256	valid
1.0ms	6×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify177.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	78	31
1	78	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: 15.1b

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)
0.6b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_98`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`add-log-exp_binary64_113`
2×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10`
1×	`sin-mult_binary64_229` `acos-asin_binary64_255` `sub-neg_binary64_70` `cos-sum_binary64_208` `cos-diff_binary64_211`

Counts

4 → 54

Calls

4 calls:

5.0ms	(*.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)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series558.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

387.0ms	(.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)
70.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
69.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4958	1438
1	4958	1438

prune104.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	50	16	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	16	67

Merged error: 2.9b

Counts

67 → 16

Compiler

Compiled 2130 to 586 computations (72.5% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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)
0.6b	(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))))))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_98`
10×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`add-log-exp_binary64_113`
3×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10`
2×	`sin-mult_binary64_229`
1×	`acos-asin_binary64_255`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.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)
1.0ms	(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))))))

series603.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

354.0ms	(.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)
100.0ms	(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))))))
80.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
68.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5004	1948

prune129.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	75	17	92

Merged error: 2.7b

Counts

92 → 17

Compiler

Compiled 3111 to 719 computations (76.9% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (exp.f64 (log.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)
0.6b	(log.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)))))))
0.6b	(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))))))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_98`
10×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`associate-l_binary64_20` `pow1_binary64_135`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
7×	`log-prod_binary64_160`
6×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `exp-sum_binary64_120`
3×	`unswap-sqr_binary64_45`
2×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `*-commutative_binary64_10`
1×	`rem-log-exp_binary64_115` `sin-mult_binary64_229` `acos-asin_binary64_255` `log-pow_binary64_163`

Counts

4 → 61

Calls

4 calls:

7.0ms	(.f64 (exp.f64 (log.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)
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(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))))))
1.0ms	(log.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)))))))

series1.2s (7.1%)

Counts

4 → 12

Calls

4 calls:

783.0ms	(.f64 (exp.f64 (log.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)
230.0ms	(log.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)))))))
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)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
73.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4898	2649
1	4898	2649

prune123.0ms (0.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	71	19	90

Merged error: 2.7b

Counts

90 → 19

Compiler

Compiled 3428 to 791 computations (76.9% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
0.4b	(asin.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))))))
0.7b	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_98`
12×	`*-un-lft-identity_binary64_77`
9×	`associate-l_binary64_20`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `add-cube-cbrt_binary64_109`
6×	`add-log-exp_binary64_113` `associate-r_binary64_19`
4×	`difference-of-squares_binary64_46`
2×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `distribute-lft-out--_binary64_31` `times-frac_binary64_83` `associate-l/_binary64_22` `flip--_binary64_52` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `-commutative_binary64_10` `asin-acos_binary64_254` `flip3--_binary64_81`
1×	`sin-mult_binary64_229` `associate--r-_binary64_18` `sub-neg_binary64_70` `diff-log_binary64_166`

Counts

4 → 65

Calls

4 calls:

12.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
9.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(asin.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))))))

series896.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

554.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
179.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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)))))))
96.0ms	(asin.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))))))
66.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5066	3362

prune117.0ms (0.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	75	21	96

Merged error: 2.5b

Counts

96 → 21

Compiler

Compiled 3257 to 637 computations (80.4% saved)

regimes513.0ms (3.1%)

Compiler: Compiled 7677 to 4200 computations (45.3% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	197	57
1	197	57

end0.0ms (0%)

sample8.5s (51.3%)

Algorithm

1×

intervals

Results

5.6s	5546×	body	1024	valid
782.0ms	1342×	body	512	valid
651.0ms	272×	body	2048	valid
188.0ms	500×	body	256	valid
63.0ms	340×	body	128	valid
4.0ms	4×	body	1024	invalid

Compiler

Compiled 1109 to 610 computations (45% saved)

Details

analyze2.8s (16.9%)

sample258.0ms (1.6%)

simplify177.0ms (1.1%)

prune3.0ms (0%)

localize28.0ms (0.2%)

rewrite21.0ms (0.1%)

series558.0ms (3.4%)

simplify72.0ms (0.4%)

prune104.0ms (0.6%)

localize35.0ms (0.2%)

rewrite24.0ms (0.1%)

series603.0ms (3.7%)

simplify86.0ms (0.5%)

prune129.0ms (0.8%)

localize36.0ms (0.2%)

rewrite24.0ms (0.1%)

series1.2s (7.1%)

simplify95.0ms (0.6%)

prune123.0ms (0.7%)

localize35.0ms (0.2%)

rewrite38.0ms (0.2%)

series896.0ms (5.4%)

simplify80.0ms (0.5%)

prune117.0ms (0.7%)

regimes513.0ms (3.1%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample8.5s (51.3%)

Profiling