Details

analyze3.0s (17.6%)

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)

sample253.0ms (1.5%)

Algorithm

1×

intervals

Results

177.0ms	175×	body	1024	valid
26.0ms	10×	body	2048	valid
25.0ms	43×	body	512	valid
7.0ms	19×	body	256	valid
2.0ms	9×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify180.0ms (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: 18.6b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize24.0ms (0.1%)

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)
1.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (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)))))

series396.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(.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)
81.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
68.0ms	(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 (54.0ms)

Iter	Nodes	Cost
0	4958	1438
1	4958	1438

prune99.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	53	13	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	13	67

Merged error: 5.5b

Counts

67 → 13

Compiler

Compiled 2044 to 525 computations (74.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.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)
1.7b	(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))))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `add-sqr-sqrt_binary64_98`
9×	`add-cube-cbrt_binary64_109` `-un-lft-identity_binary64_77` `associate-r*_binary64_19`
7×	`associate-l_binary64_20`
6×	`cos-mult_binary64_228`
5×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
4×	`add-log-exp_binary64_113`
3×	`sin-mult_binary64_229` `frac-times_binary64_87` `associate-r/_binary64_21` `-commutative_binary64_10`
2×	`frac-add_binary64_85` `flip-+_binary64_51` `flip3-+_binary64_80` `unswap-sqr_binary64_45`
1×	`acos-asin_binary64_255` `distribute-lft-in_binary64_28` `associate-*l/_binary64_22` `distribute-rgt-in_binary64_29`

Counts

4 → 72

Calls

4 calls:

12.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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))))))

series926.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

426.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
337.0ms	(.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)
96.0ms	(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))))))
67.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5005	2773

prune148.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	15	84
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	80	17	97

Merged error: 5.4b

Counts

97 → 17

Compiler

Compiled 3650 to 827 computations (77.3% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.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)
0.4b	(exp.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)))))))
1.2b	(log.f64 (exp.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))))))))
1.7b	(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))))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_98`
10×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`exp-prod_binary64_126`
8×	`pow1_binary64_135` `log-pow_binary64_163`
7×	`associate-l_binary64_20`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
5×	`add-log-exp_binary64_113`
3×	`log-prod_binary64_160` `acos-asin_binary64_255` `associate-r_binary64_19`
2×	`exp-diff_binary64_122`
1×	`rem-log-exp_binary64_115` `pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `log-div_binary64_161` `rem-exp-log_binary64_114`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (log.f64 (exp.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)
3.0ms	(log.f64 (exp.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))))))))
2.0ms	(exp.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)))))))
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))))))

series1.4s (8.1%)

Counts

4 → 12

Calls

4 calls:

754.0ms	(.f64 (log.f64 (exp.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)
324.0ms	(log.f64 (exp.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))))))))
195.0ms	(exp.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)))))))
87.0ms	(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))))))

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4865	3226
1	4865	3226

prune126.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Merged error: 5.4b

Counts

87 → 17

Compiler

Compiled 3631 to 648 computations (82.2% saved)

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
0.6b	(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
1.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.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))))))))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`pow1_binary64_135`
22×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
19×	`pow-prod-down_binary64_145`
10×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
6×	`pow-unpow_binary64_151` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
5×	`cos-mult_binary64_228`
4×	`rem-cube-cbrt_binary64_99` `add-log-exp_binary64_113` `pow-sqr_binary64_50` `pow-prod-up_binary64_144` `pow-exp_binary64_142` `pow-pow_binary64_146`
2×	`pow-to-exp_binary64_143` `cube-div_binary64_103` `pow-plus_binary64_137` `sqr-pow_binary64_49` `cube-mult_binary64_104` `unpow-prod-down_binary64_153` `cube-prod_binary64_102` `unpow3_binary64_140`
1×	`pow2_binary64_155` `associate-l_binary64_20` `sin-mult_binary64_229` `acos-asin_binary64_255` `frac-times_binary64_87` `associate-l/_binary64_22` `associate-r/_binary64_21` `-commutative_binary64_10` `swap-sqr_binary64_44` `associate-r*_binary64_19`

Counts

4 → 91

Calls

4 calls:

10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
5.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
5.0ms	(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.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))))))))

series934.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

579.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.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))))))))
139.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
119.0ms	(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
97.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5141	2243

prune197.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	105	15	120

Merged error: 5.4b

Counts

120 → 15

Compiler

Compiled 7147 to 1430 computations (80% saved)

regimes369.0ms (2.2%)

Compiler: Compiled 5792 to 2862 computations (50.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	109
1	100	109

end0.0ms (0%)

sample8.3s (49.4%)

Algorithm

1×

intervals

Results

5.6s	5520×	body	1024	valid
853.0ms	1418×	body	512	valid
640.0ms	249×	body	2048	valid
195.0ms	501×	body	256	valid
58.0ms	312×	body	128	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 910 to 453 computations (50.2% saved)

Details

analyze3.0s (17.6%)

sample253.0ms (1.5%)

simplify180.0ms (1.1%)

prune3.0ms (0%)

localize24.0ms (0.1%)

rewrite20.0ms (0.1%)

series396.0ms (2.4%)

simplify72.0ms (0.4%)

prune99.0ms (0.6%)

localize30.0ms (0.2%)

rewrite31.0ms (0.2%)

series926.0ms (5.5%)

simplify79.0ms (0.5%)

prune148.0ms (0.9%)

localize35.0ms (0.2%)

rewrite21.0ms (0.1%)

series1.4s (8.1%)

simplify91.0ms (0.5%)

prune126.0ms (0.8%)

localize46.0ms (0.3%)

rewrite40.0ms (0.2%)

series934.0ms (5.6%)

simplify69.0ms (0.4%)

prune197.0ms (1.2%)

regimes369.0ms (2.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.3s (49.4%)

Profiling