Details

analyze2.7s (15.1%)

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)

sample207.0ms (1.2%)

Algorithm

1×

intervals

Results

156.0ms	185×	body	1024	valid
20.0ms	40×	body	512	valid
8.0ms	5×	body	2048	valid
5.0ms	15×	body	256	valid
2.0ms	11×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune8.0ms (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

16.2b

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 (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)
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

series569.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

265.0ms	(.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)
141.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
105.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
57.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 1901 to 1676 computations (11.8% saved)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5016	2426

prune156.0ms (0.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	82	23	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	23	106

Error

4.8b

Counts

106 → 23

Compiler

Compiled 3201 to 1048 computations (67.3% saved)

localize27.0ms (0.2%)

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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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 lambda1) (cos.f64 lambda2)) (.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 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series831.0ms (4.7%)

Counts

4 → 44

Calls

4 calls:

389.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
158.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
151.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
132.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 2753 to 2154 computations (21.8% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4949	3144
1	4949	3144

prune173.0ms (1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	11	11	22
Picked	1	0	1
Done	0	0	0
Total	107	24	131

Error

4.7b

Counts

131 → 24

Compiler

Compiled 4325 to 1210 computations (72% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

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

series451.0ms (2.5%)

Counts

4 → 24

Calls

4 calls:

171.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
101.0ms	(cbrt.f64 (sin.f64 lambda1))
95.0ms	(cbrt.f64 (sin.f64 lambda1))
83.0ms	(cbrt.f64 (sin.f64 lambda1))

Compiler

Compiled 1691 to 1318 computations (22.1% saved)

simplify115.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4881	1302
1	4881	1302

prune118.0ms (0.7%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	23	23
Picked	0	1	1
Done	0	0	0
Total	65	24	89

Error

4.7b

Counts

89 → 24

Compiler

Compiled 3238 to 1049 computations (67.6% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
0.6b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.9b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1464`
13×	`*-un-lft-identity_binary64_1442`
9×	`associate-l_binary64_1383` `add-cube-cbrt_binary64_1477`
8×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
6×	`associate-r_binary64_1382` `add-log-exp_binary64_1481`
4×	`difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`cbrt-unprod_binary64_1475` `times-frac_binary64_1448` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `asin-acos_binary64_1622` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-l/_binary64_1385` `unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `diff-log_binary64_1534` `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 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
8.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series1.0s (5.9%)

Counts

4 → 46

Calls

4 calls:

510.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
256.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
165.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
114.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3485 to 2777 computations (20.3% saved)

simplify115.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4972	5067
1	4972	5067

prune150.0ms (0.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	9	13	22
Picked	1	0	1
Done	0	1	1
Total	117	21	138

Error

4.6b

Counts

138 → 21

Compiler

Compiled 4480 to 1123 computations (74.9% saved)

regimes2.2s (12.2%)

Accuracy

Total 0.6b remaining (15%)

Threshold costs 0.6b (15%)

Compiler

Compiled 29476 to 18298 computations (37.9% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	206	57
1	206	57

end0.0ms (0%)

sample8.6s (48%)

Algorithm

1×

intervals

Results

4.6s	5532×	body	1024	valid
722.0ms	1379×	body	512	valid
571.0ms	293×	body	2048	valid
189.0ms	501×	body	256	valid
49.0ms	295×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 2821 to 1751 computations (37.9% saved)

Details

analyze2.7s (15.1%)

sample207.0ms (1.2%)

simplify105.0ms (0.6%)

prune8.0ms (0%)

localize18.0ms (0.1%)

rewrite19.0ms (0.1%)

series569.0ms (3.2%)

simplify75.0ms (0.4%)

prune156.0ms (0.9%)

localize27.0ms (0.2%)

rewrite22.0ms (0.1%)

series831.0ms (4.7%)

simplify89.0ms (0.5%)

prune173.0ms (1%)

localize35.0ms (0.2%)

rewrite10.0ms (0.1%)

series451.0ms (2.5%)

simplify115.0ms (0.6%)

prune118.0ms (0.7%)

localize29.0ms (0.2%)

rewrite34.0ms (0.2%)

series1.0s (5.9%)

simplify115.0ms (0.6%)

prune150.0ms (0.8%)

regimes2.2s (12.2%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample8.6s (48%)

Profiling