Details

analyze4.2s (10.3%)

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)

sample439.0ms (1.1%)

Algorithm

1×

intervals

Results

279.0ms	174×	body	1024	valid
56.0ms	50×	body	512	valid
44.0ms	12×	body	2048	valid
7.0ms	11×	body	256	valid
3.0ms	9×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune7.0ms (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

17.9b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize38.0ms (0.1%)

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)
0.6b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite181.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

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:

9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
6.0ms	(.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)))))

Compiler

Compiled 1667 to 309 computations (81.5% saved)

series1.3s (3.1%)

Error

17.0b

Counts

4 → 48

Calls

4 calls:

563.0ms	(.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)
249.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
239.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
130.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2789 to 1689 computations (39.4% saved)

simplify165.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4896	2330
1	4896	2330

prune280.0ms (0.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	89	16	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Error

2.8b

Counts

106 → 16

Compiler

Compiled 2977 to 692 computations (76.8% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.7b	(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))))))

rewrite222.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

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:

10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(*.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 lambda2) (cos.f64 lambda1)) (.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 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2362 to 361 computations (84.7% saved)

series1.6s (3.9%)

Error

2.8b

Counts

4 → 46

Calls

4 calls:

882.0ms	(.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)
361.0ms	(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))))))
169.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
133.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 4077 to 2125 computations (47.9% saved)

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4843	3031
1	4843	3031

prune324.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	99	11	110
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Error

2.7b

Counts

126 → 17

Compiler

Compiled 4107 to 849 computations (79.3% saved)

localize61.0ms (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 (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))))))))
0.4b	(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)))))))))
0.7b	(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)))))))

rewrite237.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

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:

12.0ms	(.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)
5.0ms	(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)))))))))
5.0ms	(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))))))))
2.0ms	(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)

series5.3s (12.9%)

Error

2.7b

Counts

4 → 51

Calls

4 calls:

2.4s	(.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)
2.1s	(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)))))))))
395.0ms	(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))))))))
363.0ms	(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)

simplify143.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4866	4840
1	4866	4840

prune192.0ms (0.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Error

2.7b

Counts

126 → 17

Compiler

Compiled 4569 to 633 computations (86.1% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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	(asin.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)))))))
0.6b	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))

rewrite170.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

23×	`add-sqr-sqrt_binary64_1805`
13×	`*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818` `associate-l_binary64_1724`
8×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`add-log-exp_binary64_1822` `associate-r_binary64_1723`
4×	`difference-of-squares_binary64_1752`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `times-frac_binary64_1789` `distribute-lft-out--_binary64_1735` `asin-acos_binary64_1963` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `associate-l/_binary64_1726` `-commutative_binary64_1714`
1×	`diff-log_binary64_1875` `sub-neg_binary64_1776` `associate--r-_binary64_1722` `sin-mult_binary64_1938`

Counts

4 → 68

Calls

4 calls:

10.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
8.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(asin.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 3362 to 617 computations (81.6% saved)

series1.6s (3.9%)

Error

2.7b

Counts

4 → 49

Calls

4 calls:

749.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
369.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))
230.0ms	(asin.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)))))))
170.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 5093 to 2826 computations (44.5% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5044	4908

prune190.0ms (0.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	108	9	117
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	115	19	134

Error

2.4b

Counts

134 → 19

Compiler

Compiled 4454 to 815 computations (81.7% saved)

regimes8.3s (20.3%)

Accuracy

Total 0.6b remaining (15.4%)

Threshold costs 0.6b (15.4%)

Compiler

Compiled 68625 to 38133 computations (44.4% saved)

bsearch0.0ms (0%)

simplify93.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

Remove

(sort phi1 phi2)

Compiler

Compiled 192 to 138 computations (28.1% saved)

end0.0ms (0%)

sample15.6s (38.2%)

Algorithm

1×

intervals

Results

7.5s	5510×	body	1024	valid
1.2s	1447×	body	512	valid
854.0ms	262×	body	2048	valid
251.0ms	477×	body	256	valid
78.0ms	304×	body	128	valid
3.0ms	2×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 6437 to 3570 computations (44.5% saved)

Details

analyze4.2s (10.3%)

sample439.0ms (1.1%)

simplify21.0ms (0.1%)

prune7.0ms (0%)

localize38.0ms (0.1%)

rewrite181.0ms (0.4%)

series1.3s (3.1%)

simplify165.0ms (0.4%)

prune280.0ms (0.7%)

localize52.0ms (0.1%)

rewrite222.0ms (0.5%)

series1.6s (3.9%)

simplify105.0ms (0.3%)

prune324.0ms (0.8%)

localize61.0ms (0.2%)

rewrite237.0ms (0.6%)

series5.3s (12.9%)

simplify143.0ms (0.3%)

prune192.0ms (0.5%)

localize30.0ms (0.1%)

rewrite170.0ms (0.4%)

series1.6s (3.9%)

simplify108.0ms (0.3%)

prune190.0ms (0.5%)

regimes8.3s (20.3%)

bsearch0.0ms (0%)

simplify93.0ms (0.2%)

end0.0ms (0%)

sample15.6s (38.2%)

Profiling