Details

analyze3.6s (14.1%)

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)

sample245.0ms (1%)

Algorithm

1×

intervals

Results

150.0ms	166×	body	1024	valid
32.0ms	55×	body	512	valid
15.0ms	7×	body	2048	valid
6.0ms	18×	body	256	valid
2.0ms	10×	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

prune3.0ms (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

18.1b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite106.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

11×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
10×	`add-sqr-sqrt_binary64_1464`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-r_binary64_1382`
4×	`cos-sum_binary64_1576` `add-log-exp_binary64_1481` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383`
3×	`cos-diff_binary64_1579` `cancel-sign-sub-inv_binary64_1408`
2×	`*-commutative_binary64_1373`
1×	`sub-neg_binary64_1435` `acos-asin_binary64_1623` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `cos-mult_binary64_1596` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 59

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
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 1775 to 321 computations (81.9% saved)

series805.0ms (3.2%)

Error

17.8b

Counts

4 → 57

Calls

4 calls:

390.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
224.0ms	(.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)
96.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
51.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3515 to 2053 computations (41.6% saved)

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4885	2805
1	4885	2805

prune142.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	15	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	15	117

Error

4.4b

Counts

117 → 15

Compiler

Compiled 3266 to 678 computations (79.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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)
0.9b	(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))))))

rewrite137.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

13×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
9×	`add-cube-cbrt_binary64_1477` `-un-lft-identity_binary64_1442` `associate-r*_binary64_1382`
7×	`associate-l_binary64_1383`
6×	`cos-mult_binary64_1596`
5×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`add-log-exp_binary64_1481`
3×	`-commutative_binary64_1373` `sin-mult_binary64_1597` `frac-times_binary64_1452` `associate-r/_binary64_1384`
2×	`unswap-sqr_binary64_1410` `frac-add_binary64_1450` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`acos-asin_binary64_1623` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-*l/_binary64_1385`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.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 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 2888 to 452 computations (84.3% saved)

series1.4s (5.3%)

Error

4.4b

Counts

4 → 53

Calls

4 calls:

669.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
375.0ms	(.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)
167.0ms	(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))))))
86.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 4970 to 2559 computations (48.5% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5070	4363

prune183.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	109	16	125
Fresh	12	2	14
Picked	1	0	1
Done	0	0	0
Total	122	18	140

Error

4.3b

Counts

140 → 18

Compiler

Compiled 4872 to 987 computations (79.7% saved)

localize31.0ms (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 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
0.7b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

rewrite109.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

12×	`add-sqr-sqrt_binary64_1464`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`exp-prod_binary64_1494`
8×	`pow1_binary64_1503` `log-pow_binary64_1531`
7×	`associate-l_binary64_1383`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`add-log-exp_binary64_1481`
3×	`acos-asin_binary64_1623` `log-prod_binary64_1528` `associate-r_binary64_1382`
2×	`exp-diff_binary64_1490`
1×	`log-div_binary64_1529` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.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 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 2764 to 221 computations (92% saved)

series3.2s (12.4%)

Error

4.3b

Counts

4 → 51

Calls

4 calls:

1.6s	(.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 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
279.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
167.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify142.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4866	4840
1	4866	4840

prune155.0ms (0.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	108	19	127

Error

4.2b

Counts

127 → 19

Compiler

Compiled 4757 to 693 computations (85.4% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 lambda2))
0.7b	(cbrt.f64 (sin.f64 lambda2))
0.7b	(cbrt.f64 (sin.f64 lambda2))
0.9b	(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 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))

rewrite64.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

9×	`cbrt-prod_binary64_1473`
7×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1/3_binary64_1524`
1×	`acos-asin_binary64_1623`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 lambda2))
2.0ms	(cbrt.f64 (sin.f64 lambda2))
1.0ms	(cbrt.f64 (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 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))

Compiler

Compiled 1785 to 338 computations (81.1% saved)

series390.0ms (1.5%)

Error

4.2b

Counts

4 → 21

Calls

4 calls:

176.0ms	(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 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))
66.0ms	(cbrt.f64 (sin.f64 lambda2))
64.0ms	(cbrt.f64 (sin.f64 lambda2))
63.0ms	(cbrt.f64 (sin.f64 lambda2))

Compiler

Compiled 2139 to 1170 computations (45.3% saved)

simplify85.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4921	1176
1	4921	1176

prune71.0ms (0.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	63	18	81

Error

4.2b

Counts

81 → 18

Compiler

Compiled 2226 to 355 computations (84.1% saved)

regimes3.8s (15%)

Accuracy

Total 0.4b remaining (10.8%)

Threshold costs 0.4b (10.8%)

Compiler

Compiled 61544 to 33812 computations (45.1% saved)

bsearch0.0ms (0%)

simplify31.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	48
1	34	48

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 116 to 100 computations (13.8% saved)

end0.0ms (0%)

sample10.5s (41.5%)

Algorithm

1×

intervals

Results

4.9s	5521×	body	1024	valid
769.0ms	1373×	body	512	valid
515.0ms	260×	body	2048	valid
188.0ms	536×	body	256	valid
57.0ms	310×	body	128	valid
2.0ms	3×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 5700 to 3133 computations (45% saved)

Details

analyze3.6s (14.1%)

sample245.0ms (1%)

simplify12.0ms (0%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite106.0ms (0.4%)

series805.0ms (3.2%)

simplify116.0ms (0.5%)

prune142.0ms (0.6%)

localize25.0ms (0.1%)

rewrite137.0ms (0.5%)

series1.4s (5.3%)

simplify89.0ms (0.3%)

prune183.0ms (0.7%)

localize31.0ms (0.1%)

rewrite109.0ms (0.4%)

series3.2s (12.4%)

simplify142.0ms (0.6%)

prune155.0ms (0.6%)

localize33.0ms (0.1%)

rewrite64.0ms (0.3%)

series390.0ms (1.5%)

simplify85.0ms (0.3%)

prune71.0ms (0.3%)

regimes3.8s (15%)

bsearch0.0ms (0%)

simplify31.0ms (0.1%)

end0.0ms (0%)

sample10.5s (41.5%)

Profiling