Details

analyze2.7s (11.8%)

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)

sample218.0ms (0.9%)

Algorithm

1×

intervals

Results

142.0ms	175×	body	1024	valid
30.0ms	42×	body	512	valid
18.0ms	8×	body	2048	valid
6.0ms	19×	body	256	valid
2.0ms	12×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune12.0ms (0.1%)

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

17.1b

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))
0.2b	(.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)
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite95.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
4×	`cos-sum_binary64_1576` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`cos-diff_binary64_1579` `sub-neg_binary64_1435` `acos-asin_binary64_1623` `sin-mult_binary64_1597`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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 1667 to 309 computations (81.5% saved)

series550.0ms (2.4%)

Error

16.5b

Counts

4 → 47

Calls

4 calls:

245.0ms	(.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)
111.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
97.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
55.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2725 to 1648 computations (39.5% saved)

simplify109.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4901	2314
1	4901	2314

prune135.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	90	14	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Error

4.3b

Counts

105 → 14

Compiler

Compiled 2886 to 643 computations (77.7% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (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)
0.7b	(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))))))

rewrite132.0ms (0.6%)

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:

12.0ms	(.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 (6.2%)

Error

4.3b

Counts

4 → 62

Calls

4 calls:

704.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
363.0ms	(.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)
166.0ms	(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))))))
130.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5800 to 2939 computations (49.3% saved)

simplify98.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5127	4802

prune182.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	123	11	134
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	133	15	148

Error

4.2b

Counts

148 → 15

Compiler

Compiled 5087 to 1016 computations (80% saved)

localize28.0ms (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)) (+.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)
0.7b	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
27.9b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

rewrite122.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

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

series943.0ms (4.1%)

Error

4.2b

Counts

4 → 49

Calls

4 calls:

382.0ms	(.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)
228.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
152.0ms	(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))))))
130.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

Compiler

Compiled 4521 to 2492 computations (44.9% saved)

simplify84.0ms (0.4%)

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	116	0	116
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	116	15	131

Error

4.2b

Counts

131 → 15

Compiler

Compiled 4335 to 1109 computations (74.4% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
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)
0.5b	(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))))))))

rewrite144.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

23×	`add-sqr-sqrt_binary64_1464`
13×	`*-un-lft-identity_binary64_1442`
9×	`add-cube-cbrt_binary64_1477` `associate-l_binary64_1383`
8×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`add-log-exp_binary64_1481` `associate-r_binary64_1382`
4×	`difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`flip3--_binary64_1446` `flip--_binary64_1417` `times-frac_binary64_1448` `distribute-lft-out--_binary64_1394` `asin-acos_binary64_1622` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `associate-l/_binary64_1385` `-commutative_binary64_1373`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `associate--r-_binary64_1381` `sin-mult_binary64_1597`

Counts

4 → 68

Calls

4 calls:

11.0ms	(.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 lambda2) (sin.f64 lambda1))
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 674 computations (80% saved)

series1.1s (4.5%)

Error

4.2b

Counts

4 → 50

Calls

4 calls:

487.0ms	(.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)
243.0ms	(-.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))))))))
157.0ms	(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)))))))
117.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 5196 to 2907 computations (44.1% saved)

simplify105.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5029	4932

prune147.0ms (0.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	113	20	133

Error

4.0b

Counts

133 → 20

Compiler

Compiled 4495 to 904 computations (79.9% saved)

regimes4.2s (17.9%)

Accuracy

Total 0.6b remaining (14.7%)

Threshold costs 0.6b (14.7%)

Compiler

Compiled 63846 to 36468 computations (42.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

end0.0ms (0%)

sample10.4s (44.8%)

Algorithm

1×

intervals

Results

4.6s	5458×	body	1024	valid
767.0ms	1438×	body	512	valid
490.0ms	251×	body	2048	valid
182.0ms	527×	body	256	valid
54.0ms	326×	body	128	valid
2.0ms	3×	body	1024	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 5978 to 3417 computations (42.8% saved)

Details

analyze2.7s (11.8%)

sample218.0ms (0.9%)

simplify102.0ms (0.4%)

prune12.0ms (0.1%)

localize19.0ms (0.1%)

rewrite95.0ms (0.4%)

series550.0ms (2.4%)

simplify109.0ms (0.5%)

prune135.0ms (0.6%)

localize28.0ms (0.1%)

rewrite132.0ms (0.6%)

series1.4s (6.2%)

simplify98.0ms (0.4%)

prune182.0ms (0.8%)

localize28.0ms (0.1%)

rewrite122.0ms (0.5%)

series943.0ms (4.1%)

simplify84.0ms (0.4%)

prune150.0ms (0.6%)

localize27.0ms (0.1%)

rewrite144.0ms (0.6%)

series1.1s (4.5%)

simplify105.0ms (0.5%)

prune147.0ms (0.6%)

regimes4.2s (17.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample10.4s (44.8%)

Profiling