Details

analyze5.5s (17.4%)

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)

sample451.0ms (1.4%)

Algorithm

1×

intervals

Results

321.0ms	173×	body	1024	valid
50.0ms	47×	body	512	valid
39.0ms	7×	body	2048	valid
8.0ms	12×	body	256	valid
6.0ms	17×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify308.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

prune6.0ms (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: 16.9b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(.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)))))
2.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite42.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135`
9×	`add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`associate-r_binary64_19`
4×	`associate-l_binary64_20` `pow-prod-down_binary64_145` `add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
3×	`cos-diff_binary64_211`
2×	`*-commutative_binary64_10`
1×	`acos-asin_binary64_255` `sub-neg_binary64_70` `distribute-lft-in_binary64_28` `associate-*l/_binary64_22` `unswap-sqr_binary64_45` `cos-sum_binary64_208` `cos-mult_binary64_228` `distribute-rgt-in_binary64_29`

Counts

4 → 56

Calls

4 calls:

13.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
7.0ms	(.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)))))

series1.0s (3.3%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
415.0ms	(.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)
114.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
55.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify143.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4865	1670
1	4865	1670

prune185.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	12	69

Merged error: 3.3b

Counts

69 → 12

Compiler

Compiled 2104 to 513 computations (75.6% saved)

localize65.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.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)
1.0b	(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))))))

rewrite59.0ms (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:

22.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
7.0ms	(.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))))))

series1.7s (5.2%)

Counts

4 → 12

Calls

4 calls:

754.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
612.0ms	(.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)
176.0ms	(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))))))
125.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify148.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5004	2773

prune262.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 3.2b

Counts

96 → 12

Compiler

Compiled 3401 to 661 computations (80.6% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.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)))))))
0.7b	(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))))))))
1.0b	(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))))))

rewrite39.0ms (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:

11.0ms	(.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)
5.0ms	(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))))))))
4.0ms	(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)))))))
3.0ms	(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))))))

series2.5s (7.9%)

Counts

4 → 12

Calls

4 calls:

1.4s	(.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)
612.0ms	(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))))))))
357.0ms	(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)))))))
168.0ms	(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))))))

simplify178.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4865	3226
1	4865	3226

prune211.0ms (0.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	66	16	82

Merged error: 3.2b

Counts

82 → 16

Compiler

Compiled 3372 to 579 computations (82.8% saved)

localize98.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(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)
1.0b	(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))))))))

rewrite82.0ms (0.3%)

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:

19.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
11.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
10.0ms	(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
3.0ms	(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))))))))

series1.9s (5.9%)

Counts

4 → 12

Calls

4 calls:

1.1s	(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))))))))
275.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
259.0ms	(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
208.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5141	2243

prune373.0ms (1.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	13	14
Picked	0	1	1
Done	1	0	1
Total	102	17	119

Merged error: 3.2b

Counts

119 → 17

Compiler

Compiled 7147 to 1430 computations (80% saved)

regimes781.0ms (2.5%)

Compiler: Compiled 5952 to 3438 computations (42.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	109
1	100	109

end0.0ms (0%)

sample15.5s (48.8%)

Algorithm

1×

intervals

Results

10.5s	5524×	body	1024	valid
1.5s	1381×	body	512	valid
1.1s	254×	body	2048	valid
351.0ms	505×	body	256	valid
125.0ms	336×	body	128	valid
1.0ms	1×	body	512	invalid

Compiler

Compiled 902 to 519 computations (42.5% saved)

Details

analyze5.5s (17.4%)

sample451.0ms (1.4%)

simplify308.0ms (1%)

prune6.0ms (0%)

localize46.0ms (0.1%)

rewrite42.0ms (0.1%)

series1.0s (3.3%)

simplify143.0ms (0.4%)

prune185.0ms (0.6%)

localize65.0ms (0.2%)

rewrite59.0ms (0.2%)

series1.7s (5.2%)

simplify148.0ms (0.5%)

prune262.0ms (0.8%)

localize74.0ms (0.2%)

rewrite39.0ms (0.1%)

series2.5s (7.9%)

simplify178.0ms (0.6%)

prune211.0ms (0.7%)

localize98.0ms (0.3%)

rewrite82.0ms (0.3%)

series1.9s (5.9%)

simplify128.0ms (0.4%)

prune373.0ms (1.2%)

regimes781.0ms (2.5%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample15.5s (48.8%)

Profiling