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)

sample256.0ms (1.5%)

Algorithm

1×

intervals

Results

174.0ms	173×	body	1024	valid
31.0ms	45×	body	512	valid
26.0ms	11×	body	2048	valid
5.0ms	14×	body	256	valid
2.0ms	13×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify187.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

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: 15.2b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.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)
0.5b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.6b	(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)))))

series399.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(.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)
72.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
34.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4863	1492
1	4863	1492

prune432.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	14	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	14	70

Merged error: 3.0b

Counts

70 → 14

Compiler

Compiled 8588 to 4664 computations (45.7% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(*.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)
0.4b	(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))
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)
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))))))

series596.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(.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))))))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
71.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5014	1948

prune705.0ms (4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	10	3	13
Picked	0	1	1
Done	0	0	0
Total	74	16	90

Merged error: 2.9b

Counts

90 → 16

Compiler

Compiled 15263 to 7890 computations (48.3% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(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))))))))
0.3b	(.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	(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)))))))

rewrite23.0ms (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)
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))))))))
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)))))))
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 (7.8%)

Counts

4 → 12

Calls

4 calls:

767.0ms	(.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)
316.0ms	(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))))))))
200.0ms	(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))))))

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4865	3226
1	4865	3226

prune424.0ms (2.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	70	16	86

Merged error: 2.8b

Counts

86 → 16

Compiler

Compiled 10198 to 4357 computations (57.3% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_110`
23×	`add-sqr-sqrt_binary64_101`
15×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
11×	`pow1_binary64_140`
9×	`pow1/3_binary64_161`
6×	`add-exp-log_binary64_117` `associate-l_binary64_20` `swap-sqr_binary64_46` `associate-r_binary64_19`
4×	`add-cbrt-cube_binary64_115` `unswap-sqr_binary64_47` `add-log-exp_binary64_118`
2×	`pow-prod-up_binary64_149` `pow-sqr_binary64_52` `pow-prod-down_binary64_150`
1×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-plus_binary64_142` `pow2_binary64_160`

Counts

4 → 73

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))

series525.0ms (3%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
127.0ms	(cbrt.f64 (sin.f64 lambda1))
124.0ms	(cbrt.f64 (sin.f64 lambda1))
121.0ms	(cbrt.f64 (sin.f64 lambda1))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4872	797
1	4872	797

prune143.0ms (0.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	85	16	101

Merged error: 2.8b

Counts

101 → 16

Compiler

Compiled 3997 to 1129 computations (71.8% saved)

regimes365.0ms (2.1%)

Compiler: Compiled 5183 to 2855 computations (44.9% 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%)

sample8.7s (49.1%)

Algorithm

1×

intervals

Results

5.8s	5495×	body	1024	valid
877.0ms	1418×	body	512	valid
754.0ms	286×	body	2048	valid
190.0ms	494×	body	256	valid
67.0ms	307×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 783 to 442 computations (43.6% saved)

Details

analyze3.0s (17%)

sample256.0ms (1.5%)

simplify187.0ms (1.1%)

prune4.0ms (0%)

localize23.0ms (0.1%)

rewrite23.0ms (0.1%)

series399.0ms (2.3%)

simplify77.0ms (0.4%)

prune432.0ms (2.5%)

localize31.0ms (0.2%)

rewrite25.0ms (0.1%)

series596.0ms (3.4%)

simplify86.0ms (0.5%)

prune705.0ms (4%)

localize37.0ms (0.2%)

rewrite23.0ms (0.1%)

series1.4s (7.8%)

simplify95.0ms (0.5%)

prune424.0ms (2.4%)

localize35.0ms (0.2%)

rewrite24.0ms (0.1%)

series525.0ms (3%)

simplify83.0ms (0.5%)

prune143.0ms (0.8%)

regimes365.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.7s (49.1%)

Profiling