Details

analyze3.7s (14.4%)

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)

sample235.0ms (0.9%)

Algorithm

1×

intervals

Results

166.0ms	193×	body	1024	valid
19.0ms	37×	body	512	valid
7.0ms	2×	body	2048	valid
4.0ms	13×	body	256	valid
2.0ms	11×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

15.3b

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 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
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)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite107.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

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` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `cos-mult_binary64_1596` `associate-*l/_binary64_1385`

Counts

4 → 59

Calls

4 calls:

12.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.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)

series865.0ms (3.4%)

Error

14.5b

Counts

4 → 63

Calls

4 calls:

402.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
241.0ms	(.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)
107.0ms	(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 3879 to 2186 computations (43.6% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4968	3094
1	4968	3094

prune150.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Error

1.9b

Counts

123 → 13

Compiler

Compiled 3479 to 730 computations (79% 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))))
0.3b	(.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))))))

rewrite139.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

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))
3.0ms	(.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 (5.6%)

Error

1.9b

Counts

4 → 62

Calls

4 calls:

719.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
372.0ms	(.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)
154.0ms	(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))))))
117.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5800 to 2939 computations (49.3% saved)

simplify93.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5127	4802

prune183.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	120	14	134
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	132	15	147

Error

1.8b

Counts

147 → 15

Compiler

Compiled 5203 to 1028 computations (80.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
0.3b	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
28.9b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

rewrite115.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`add-cube-cbrt_binary64_1477` `cbrt-prod_binary64_1473` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481`
3×	`pow-unpow_binary64_1519` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`sin-mult_binary64_1597` `cube-div_binary64_1471` `unpow-prod-down_binary64_1521` `unpow3_binary64_1508` `cube-mult_binary64_1472` `cube-prod_binary64_1470` `sqr-pow_binary64_1414` `pow-prod-down_binary64_1513` `pow-pow_binary64_1514` `prod-exp_binary64_1491` `pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `cbrt-unprod_binary64_1475`
1×	`pow1/3_binary64_1524` `cbrt-div_binary64_1474` `rem-cbrt-cube_binary64_1466` `acos-asin_binary64_1623` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 67

Calls

4 calls:

5.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))
3.0ms	(.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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) 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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))

Compiler

Compiled 2752 to 882 computations (68% saved)

series912.0ms (3.6%)

Error

1.8b

Counts

4 → 49

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 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
231.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
158.0ms	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
118.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

Compiler

Compiled 4521 to 2492 computations (44.9% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4946	3251
1	4946	3251

prune150.0ms (0.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	116	15	131

Error

1.8b

Counts

131 → 15

Compiler

Compiled 4457 to 1133 computations (74.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
0.3b	(.f64 (exp.f64 (log.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)
0.7b	(log.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)))))))

rewrite103.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

16×	`add-sqr-sqrt_binary64_1464`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`pow1_binary64_1503` `associate-l_binary64_1383`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
7×	`log-prod_binary64_1528`
6×	`associate-r_binary64_1382`
4×	`add-log-exp_binary64_1481` `exp-sum_binary64_1488`
3×	`unswap-sqr_binary64_1410`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `*-commutative_binary64_1373`
1×	`acos-asin_binary64_1623` `log-pow_binary64_1531` `rem-log-exp_binary64_1483` `sin-mult_binary64_1597`

Counts

4 → 61

Calls

4 calls:

6.0ms	(.f64 (exp.f64 (log.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)
5.0ms	(*.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)))))))
1.0ms	(log.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))))))))

Compiler

Compiled 2668 to 382 computations (85.7% saved)

series2.8s (11%)

Error

1.8b

Counts

4 → 50

Calls

4 calls:

1.5s	(.f64 (exp.f64 (log.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)
934.0ms	(log.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))))))))
164.0ms	(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)))))))
118.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 4908 to 2546 computations (48.1% saved)

simplify135.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4822	4038
1	4822	4038

prune114.0ms (0.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	111	15	126

Error

1.8b

Counts

126 → 15

Compiler

Compiled 3753 to 467 computations (87.6% saved)

regimes3.4s (13.6%)

Accuracy

Total 0.4b remaining (10.4%)

Threshold costs 0.4b (10.4%)

Compiler

Compiled 53431 to 31561 computations (40.9% saved)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	65
1	38	65

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 156 to 108 computations (30.8% saved)

end0.0ms (0%)

sample10.4s (41.1%)

Algorithm

1×

intervals

Results

5.0s	5569×	body	1024	valid
794.0ms	1428×	body	512	valid
435.0ms	211×	body	2048	valid
179.0ms	497×	body	256	valid
57.0ms	295×	body	128	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 4917 to 2921 computations (40.6% saved)

Details

analyze3.7s (14.4%)

sample235.0ms (0.9%)

simplify11.0ms (0%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite107.0ms (0.4%)

series865.0ms (3.4%)

simplify87.0ms (0.3%)

prune150.0ms (0.6%)

localize25.0ms (0.1%)

rewrite139.0ms (0.5%)

series1.4s (5.6%)

simplify93.0ms (0.4%)

prune183.0ms (0.7%)

localize29.0ms (0.1%)

rewrite115.0ms (0.5%)

series912.0ms (3.6%)

simplify83.0ms (0.3%)

prune150.0ms (0.6%)

localize29.0ms (0.1%)

rewrite103.0ms (0.4%)

series2.8s (11%)

simplify135.0ms (0.5%)

prune114.0ms (0.4%)

regimes3.4s (13.6%)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample10.4s (41.1%)

Profiling