Details

analyze3.8s (17.4%)

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)

sample245.0ms (1.1%)

Algorithm

1×

intervals

Results

147.0ms	172×	body	1024	valid
36.0ms	12×	body	2048	valid
22.0ms	43×	body	512	valid
6.0ms	19×	body	256	valid
2.0ms	10×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify12.0ms (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

16.3b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize20.0ms (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)
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)))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite101.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

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))
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)))))

Compiler

Compiled 1667 to 309 computations (81.5% saved)

series553.0ms (2.6%)

Error

15.6b

Counts

4 → 48

Calls

4 calls:

246.0ms	(.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)
115.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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)))))
46.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2795 to 1687 computations (39.6% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	2354
1	4964	2354

prune132.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	91	14	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	14	106

Error

2.7b

Counts

106 → 14

Compiler

Compiled 2949 to 671 computations (77.2% saved)

localize24.0ms (0.1%)

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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.8b	(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))))))

rewrite110.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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 2362 to 361 computations (84.7% saved)

series843.0ms (3.9%)

Error

2.7b

Counts

4 → 51

Calls

4 calls:

383.0ms	(.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)
156.0ms	(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))))))
124.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
124.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4448 to 2323 computations (47.8% saved)

simplify95.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5034	3160

prune168.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	101	14	115
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	112	17	129

Error

2.6b

Counts

129 → 17

Compiler

Compiled 4282 to 939 computations (78.1% 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 (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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
0.8b	(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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
2.9b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))

rewrite90.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
5×	`add-log-exp_binary64_1481`
3×	`log-pow_binary64_1531` `log-prod_binary64_1528`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`exp-to-pow_binary64_1504` `exp-prod_binary64_1494` `rem-log-exp_binary64_1483` `acos-asin_binary64_1623` `sin-mult_binary64_1597`

Counts

4 → 59

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
2.0ms	(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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 2357 to 375 computations (84.1% saved)

series1.1s (5%)

Error

2.6b

Counts

4 → 51

Calls

4 calls:

371.0ms	(.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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
368.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
165.0ms	(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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
119.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 4690 to 2503 computations (46.6% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5000	3113

prune143.0ms (0.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	109	18	127

Error

2.6b

Counts

127 → 18

Compiler

Compiled 4265 to 997 computations (76.6% saved)

localize27.0ms (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)
0.8b	(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))))))
24.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

rewrite119.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

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)

series930.0ms (4.3%)

Error

2.6b

Counts

4 → 51

Calls

4 calls:

367.0ms	(.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)
227.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
155.0ms	(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))))))
125.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

Compiler

Compiled 4636 to 2550 computations (45% saved)

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5041	3323

prune123.0ms (0.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	16	16
Picked	1	0	1
Done	0	1	1
Total	118	18	136

Error

2.6b

Counts

136 → 18

Compiler

Compiled 3880 to 816 computations (79% saved)

regimes2.9s (13.6%)

Accuracy

Total 0.4b remaining (9.6%)

Threshold costs 0.4b (9.6%)

Compiler

Compiled 45065 to 26735 computations (40.7% saved)

bsearch0.0ms (0%)

simplify30.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	47
1	33	47

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 112 to 96 computations (14.3% saved)

end0.0ms (0%)

sample9.8s (45.3%)

Algorithm

1×

intervals

Results

4.8s	5499×	body	1024	valid
787.0ms	1419×	body	512	valid
471.0ms	246×	body	2048	valid
183.0ms	532×	body	256	valid
56.0ms	304×	body	128	valid
1.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 4115 to 2465 computations (40.1% saved)

Details

analyze3.8s (17.4%)

sample245.0ms (1.1%)

simplify12.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite101.0ms (0.5%)

series553.0ms (2.6%)

simplify76.0ms (0.4%)

prune132.0ms (0.6%)

localize24.0ms (0.1%)

rewrite110.0ms (0.5%)

series843.0ms (3.9%)

simplify95.0ms (0.4%)

prune168.0ms (0.8%)

localize27.0ms (0.1%)

rewrite90.0ms (0.4%)

series1.1s (5%)

simplify94.0ms (0.4%)

prune143.0ms (0.7%)

localize27.0ms (0.1%)

rewrite119.0ms (0.5%)

series930.0ms (4.3%)

simplify87.0ms (0.4%)

prune123.0ms (0.6%)

regimes2.9s (13.6%)

bsearch0.0ms (0%)

simplify30.0ms (0.1%)

end0.0ms (0%)

sample9.8s (45.3%)

Profiling