Details

analyze3.0s (17%)

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)

sample254.0ms (1.5%)

Algorithm

1×

intervals

Results

183.0ms	172×	body	1024	valid
28.0ms	51×	body	512	valid
20.0ms	8×	body	2048	valid
6.0ms	16×	body	256	valid
2.0ms	9×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify170.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

prune4.0ms (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: 16.0b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.5b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
6×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`cos-sum_binary64_213` `add-log-exp_binary64_118`
3×	`cancel-sign-sub-inv_binary64_45`
2×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150`
1×	`sin-mult_binary64_234` `cos-diff_binary64_216` `acos-asin_binary64_260` `sub-neg_binary64_72`

Counts

4 → 57

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
6.0ms	(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)))))

series394.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(.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)
71.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
67.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4863	1492
1	4863	1492

prune497.0ms (2.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	54	15	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	15	70

Merged error: 2.9b

Counts

70 → 15

Compiler

Compiled 9665 to 5514 computations (42.9% 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))
0.2b	(.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)
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))))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_101`
10×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-cube-cbrt_binary64_114` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
9×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`add-log-exp_binary64_118`
3×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150`
2×	`sin-mult_binary64_234`
1×	`acos-asin_binary64_260`

Counts

4 → 64

Calls

4 calls:

6.0ms	(*.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))))))

series580.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(.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)
90.0ms	(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))))))
74.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
68.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5014	1948

prune636.0ms (3.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	73	18	91

Merged error: 2.8b

Counts

91 → 18

Compiler

Compiled 13290 to 6959 computations (47.6% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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)) (log.f64 (exp.f64 (.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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
4.1b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
8×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
6×	`associate-l_binary64_20` `associate-r_binary64_19`
5×	`add-log-exp_binary64_118`
3×	`log-prod_binary64_165` `log-pow_binary64_168`
2×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150`
1×	`rem-log-exp_binary64_120` `sin-mult_binary64_234` `exp-prod_binary64_131` `acos-asin_binary64_260` `exp-to-pow_binary64_141`

Counts

4 → 59

Calls

4 calls:

6.0ms	(*.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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
2.0ms	(log.f64 (exp.f64 (*.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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series684.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

346.0ms	(.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)
167.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
95.0ms	(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))))))))
76.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4961	1901
1	4961	1901

prune183.0ms (1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	15	16
Picked	0	1	1
Done	0	1	1
Total	71	18	89

Merged error: 2.8b

Counts

89 → 18

Compiler

Compiled 4435 to 1617 computations (63.5% saved)

localize37.0ms (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	(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))))))))
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)))))))
0.6b	(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))))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_101`
10×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
9×	`exp-prod_binary64_131`
8×	`log-pow_binary64_168` `pow1_binary64_140`
7×	`associate-l_binary64_20`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
5×	`add-log-exp_binary64_118`
3×	`log-prod_binary64_165` `acos-asin_binary64_260` `associate-r_binary64_19`
2×	`exp-diff_binary64_127`
1×	`rem-log-exp_binary64_120` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `log-div_binary64_166` `rem-exp-log_binary64_119`

Counts

4 → 58

Calls

4 calls:

7.0ms	(.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))))))))
3.0ms	(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)))))))
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))))))

series1.3s (7.7%)

Counts

4 → 12

Calls

4 calls:

743.0ms	(.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)
327.0ms	(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))))))))
189.0ms	(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)))))))
81.0ms	(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))))))

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4865	3226
1	4865	3226

prune350.0ms (2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	3	12	15
Picked	1	0	1
Done	0	2	2
Total	69	19	88

Merged error: 2.8b

Counts

88 → 19

Compiler

Compiled 8277 to 3485 computations (57.9% saved)

regimes458.0ms (2.6%)

Compiler: Compiled 6122 to 3538 computations (42.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample8.4s (48%)

Algorithm

1×

intervals

Results

5.6s	5487×	body	1024	valid
861.0ms	1428×	body	512	valid
701.0ms	287×	body	2048	valid
186.0ms	507×	body	256	valid
54.0ms	291×	body	128	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 854 to 495 computations (42% saved)

Details

analyze3.0s (17%)

sample254.0ms (1.5%)

simplify170.0ms (1%)

prune4.0ms (0%)

localize30.0ms (0.2%)

rewrite23.0ms (0.1%)

series394.0ms (2.2%)

simplify76.0ms (0.4%)

prune497.0ms (2.8%)

localize35.0ms (0.2%)

rewrite25.0ms (0.1%)

series580.0ms (3.3%)

simplify87.0ms (0.5%)

prune636.0ms (3.6%)

localize35.0ms (0.2%)

rewrite21.0ms (0.1%)

series684.0ms (3.9%)

simplify98.0ms (0.6%)

prune183.0ms (1%)

localize37.0ms (0.2%)

rewrite25.0ms (0.1%)

series1.3s (7.7%)

simplify94.0ms (0.5%)

prune350.0ms (2%)

regimes458.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.4s (48%)

Profiling