Details

analyze2.8s (17.5%)

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)

sample208.0ms (1.3%)

Algorithm

1×

intervals

Results

146.0ms	177×	body	1024	valid
25.0ms	49×	body	512	valid
14.0ms	7×	body	2048	valid
4.0ms	13×	body	256	valid
2.0ms	10×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

15.0b

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)
0.3b	(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))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

series297.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(.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)
116.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
37.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4894	1724
1	4894	1724

prune102.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	57	14	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Error

3.1b

Counts

72 → 14

Compiler

Compiled 2216 to 551 computations (75.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
0.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
12×	`add-sqr-sqrt_binary64_1464`
10×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`associate-r_binary64_1382` `associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481`
3×	`*-commutative_binary64_1373` `sin-mult_binary64_1597`
2×	`cos-mult_binary64_1596` `unswap-sqr_binary64_1410`
1×	`associate-r/_binary64_1384` `acos-asin_binary64_1623` `frac-times_binary64_1452` `associate-l/_binary64_1385`

Counts

4 → 70

Calls

4 calls:

9.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))

series400.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
117.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
59.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))
38.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4950	2261
1	4950	2261

prune137.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	78	18	96

Error

3.0b

Counts

96 → 18

Compiler

Compiled 3683 to 806 computations (78.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
0.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.9b	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1_binary64_1503`
18×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `add-sqr-sqrt_binary64_1464` `prod-exp_binary64_1491`
7×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
5×	`add-log-exp_binary64_1481`
4×	`associate-r_binary64_1382` `associate-l_binary64_1383`
3×	`log-prod_binary64_1528` `log-pow_binary64_1531`
2×	`*-commutative_binary64_1373` `cos-mult_binary64_1596` `sin-mult_binary64_1597`
1×	`associate-r/_binary64_1384` `acos-asin_binary64_1623` `rem-log-exp_binary64_1483` `exp-prod_binary64_1494` `frac-times_binary64_1452` `exp-to-pow_binary64_1504` `associate-l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 65

Calls

4 calls:

9.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
3.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series620.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
209.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
120.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
59.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5734	2387

prune118.0ms (0.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Error

3.0b

Counts

95 → 16

Compiler

Compiled 3561 to 753 computations (78.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.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 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.4b	(-.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 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

rewrite36.0ms (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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
10.0ms	(-.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 (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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

series512.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(.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 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
103.0ms	(-.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 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
55.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
38.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5050	3373

prune109.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	78	18	96

Error

2.8b

Counts

96 → 18

Compiler

Compiled 3282 to 672 computations (79.5% saved)

regimes1.6s (9.9%)

Accuracy

Total 0.6b remaining (14.4%)

Threshold costs 0.6b (14.4%)

Compiler

Compiled 24378 to 14714 computations (39.6% 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%)

sample8.6s (52.9%)

Algorithm

1×

intervals

Results

4.7s	5498×	body	1024	valid
968.0ms	1417×	body	512	valid
491.0ms	247×	body	2048	valid
182.0ms	505×	body	256	valid
58.0ms	333×	body	128	valid
4.0ms	4×	body	1024	invalid

Compiler

Compiled 2344 to 1411 computations (39.8% saved)

Details

analyze2.8s (17.5%)

sample208.0ms (1.3%)

simplify110.0ms (0.7%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite21.0ms (0.1%)

series297.0ms (1.8%)

simplify80.0ms (0.5%)

prune102.0ms (0.6%)

localize30.0ms (0.2%)

rewrite27.0ms (0.2%)

series400.0ms (2.5%)

simplify108.0ms (0.7%)

prune137.0ms (0.8%)

localize30.0ms (0.2%)

rewrite25.0ms (0.2%)

series620.0ms (3.8%)

simplify65.0ms (0.4%)

prune118.0ms (0.7%)

localize28.0ms (0.2%)

rewrite36.0ms (0.2%)

series512.0ms (3.2%)

simplify98.0ms (0.6%)

prune109.0ms (0.7%)

regimes1.6s (9.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.6s (52.9%)

Profiling