Details

analyze3.0s (19.2%)

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

Compiler

Compiled 20 to 18 computations (10% saved)

sample225.0ms (1.4%)

Algorithm

1×

intervals

Results

161.0ms	180×	body	1024	valid
19.0ms	38×	body	512	valid
18.0ms	9×	body	2048	valid
7.0ms	21×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify11.0ms (0.1%)

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

14.9b

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))
0.3b	(.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)
1.6b	(cos.f64 (-.f64 lambda1 lambda2))
1.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (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))
4.0ms	(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)))))

series202.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.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)
37.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
36.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4809	1492
1	4809	1492

prune93.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	11	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Error

2.8b

Counts

70 → 11

Compiler

Compiled 2106 to 476 computations (77.4% saved)

localize25.0ms (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))
0.3b	(.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)
1.7b	(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))))))

rewrite21.0ms (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))
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 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))))))

series320.0ms (2%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(.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)
57.0ms	(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))))))
40.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
36.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5083	1948

prune118.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	72	15	87

Error

2.7b

Counts

87 → 15

Compiler

Compiled 3114 to 682 computations (78.1% 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 (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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
1.7b	(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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
4.4b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
6×	`associate-r_binary64_1382` `associate-l_binary64_1383`
5×	`add-log-exp_binary64_1481`
3×	`log-prod_binary64_1528` `log-pow_binary64_1531`
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` `rem-log-exp_binary64_1483` `exp-prod_binary64_1494` `exp-to-pow_binary64_1504` `sin-mult_binary64_1597`

Counts

4 → 59

Calls

4 calls:

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 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (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 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series372.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(.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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
79.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
60.0ms	(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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
36.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4926	1901
1	4926	1901

prune106.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	71	15	86

Error

2.7b

Counts

86 → 15

Compiler

Compiled 2996 to 697 computations (76.7% saved)

localize27.0ms (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 (.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))))))
1.3b	(-.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:

10.0ms	(.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))
2.0ms	(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))))))

series494.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(.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)
104.0ms	(-.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)))))))
50.0ms	(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))))))
37.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5049	3373

prune106.0ms (0.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	77	18	95

Error

2.5b

Counts

95 → 18

Compiler

Compiled 3282 to 654 computations (80.1% saved)

regimes1.6s (10.2%)

Accuracy

Total 0.5b remaining (14.9%)

Threshold costs 0.5b (14.9%)

Compiler

Compiled 24866 to 14540 computations (41.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample8.5s (54.1%)

Algorithm

1×

intervals

Results

4.8s	5481×	body	1024	valid
793.0ms	1427×	body	512	valid
499.0ms	240×	body	2048	valid
186.0ms	536×	body	256	valid
54.0ms	316×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 2283 to 1331 computations (41.7% saved)

Details

analyze3.0s (19.2%)

sample225.0ms (1.4%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite19.0ms (0.1%)

series202.0ms (1.3%)

simplify78.0ms (0.5%)

prune93.0ms (0.6%)

localize25.0ms (0.2%)

rewrite21.0ms (0.1%)

series320.0ms (2%)

simplify77.0ms (0.5%)

prune118.0ms (0.8%)

localize30.0ms (0.2%)

rewrite19.0ms (0.1%)

series372.0ms (2.4%)

simplify82.0ms (0.5%)

prune106.0ms (0.7%)

localize27.0ms (0.2%)

rewrite34.0ms (0.2%)

series494.0ms (3.2%)

simplify93.0ms (0.6%)

prune106.0ms (0.7%)

regimes1.6s (10.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.5s (54.1%)

Profiling