Details

analyze3.6s (14.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2392	341
1	2392	341
0	5	5
1	5	5

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

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample464.0ms (1.9%)

Algorithm

1×

intervals

Results

389.0ms	186×	body	1024	valid
25.0ms	45×	body	512	valid
10.0ms	5×	body	2048	valid
5.0ms	15×	body	256	valid
1.0ms	5×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	96	31
1	96	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

Error

17.2b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize19.0ms (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)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite97.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

Rules

13×	`add-sqr-sqrt_binary64_1805`
9×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`cos-sum_binary64_1917` `add-log-exp_binary64_1822`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
1×	`cos-diff_binary64_1920` `sub-neg_binary64_1776` `acos-asin_binary64_1964` `sin-mult_binary64_1938`

Counts

4 → 57

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)))))

Compiler

Compiled 1667 to 309 computations (81.5% saved)

series548.0ms (2.2%)

Error

16.4b

Counts

4 → 49

Calls

4 calls:

236.0ms	(.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)
120.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
95.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
54.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2874 to 1739 computations (39.5% saved)

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4825	2354
1	4825	2354

prune127.0ms (0.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Error

3.4b

Counts

107 → 11

Compiler

Compiled 2887 to 605 computations (79% saved)

localize25.0ms (0.1%)

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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite108.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

16×	`add-sqr-sqrt_binary64_1805`
10×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822`
3×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
2×	`sin-mult_binary64_1938`
1×	`acos-asin_binary64_1964`

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 lambda2) (cos.f64 lambda1)) (.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 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2362 to 361 computations (84.7% saved)

series778.0ms (3.2%)

Error

3.4b

Counts

4 → 47

Calls

4 calls:

368.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
144.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
123.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
98.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 4172 to 2179 computations (47.8% saved)

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4985	3055
1	4985	3055

prune152.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Error

3.3b

Counts

122 → 15

Compiler

Compiled 4063 to 827 computations (79.6% saved)

localize28.0ms (0.1%)

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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.5b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite104.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

12×	`add-sqr-sqrt_binary64_1805`
10×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`exp-prod_binary64_1835`
8×	`pow1_binary64_1844` `log-pow_binary64_1872`
7×	`associate-l_binary64_1724`
6×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
5×	`add-log-exp_binary64_1822`
3×	`acos-asin_binary64_1964` `log-prod_binary64_1869` `associate-r_binary64_1723`
2×	`exp-diff_binary64_1831`
1×	`log-div_binary64_1870` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`

Counts

4 → 58

Calls

4 calls:

8.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 2764 to 221 computations (92% saved)

series3.1s (12.7%)

Error

3.3b

Counts

4 → 51

Calls

4 calls:

1.5s	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
1.1s	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
263.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
155.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify144.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4866	4840
1	4866	4840

prune146.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	106	18	124

Error

3.3b

Counts

124 → 18

Compiler

Compiled 4615 to 653 computations (85.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
8.3b	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
8.3b	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
8.3b	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))

rewrite72.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

4×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
3×	`pow1/3_binary64_1865` `sin-mult_binary64_1938` `cbrt-div_binary64_1815` `cbrt-prod_binary64_1814`
1×	`acos-asin_binary64_1964`

Counts

4 → 38

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
4.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
3.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 1950 to 299 computations (84.7% saved)

series863.0ms (3.5%)

Error

3.3b

Counts

4 → 30

Calls

4 calls:

230.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
215.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
212.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
174.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 3552 to 1821 computations (48.7% saved)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5807	1401

prune78.0ms (0.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	68	18	86

Error

3.3b

Counts

86 → 18

Compiler

Compiled 2736 to 350 computations (87.2% saved)

regimes3.4s (14%)

Accuracy

Total 0.4b remaining (10.5%)

Threshold costs 0.4b (10.5%)

Compiler

Compiled 52597 to 30961 computations (41.1% saved)

bsearch0.0ms (0%)

simplify30.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 104 to 88 computations (15.4% saved)

end0.0ms (0%)

sample10.2s (41.9%)

Algorithm

1×

intervals

Results

4.9s	5582×	body	1024	valid
764.0ms	1421×	body	512	valid
465.0ms	242×	body	2048	valid
167.0ms	464×	body	256	valid
49.0ms	291×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 4898 to 2896 computations (40.9% saved)

Details

analyze3.6s (14.7%)

sample464.0ms (1.9%)

simplify12.0ms (0%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite97.0ms (0.4%)

series548.0ms (2.2%)

simplify96.0ms (0.4%)

prune127.0ms (0.5%)

localize25.0ms (0.1%)

rewrite108.0ms (0.4%)

series778.0ms (3.2%)

simplify89.0ms (0.4%)

prune152.0ms (0.6%)

localize28.0ms (0.1%)

rewrite104.0ms (0.4%)

series3.1s (12.7%)

simplify144.0ms (0.6%)

prune146.0ms (0.6%)

localize29.0ms (0.1%)

rewrite72.0ms (0.3%)

series863.0ms (3.5%)

simplify80.0ms (0.3%)

prune78.0ms (0.3%)

regimes3.4s (14%)

bsearch0.0ms (0%)

simplify30.0ms (0.1%)

end0.0ms (0%)

sample10.2s (41.9%)

Profiling