Details

analyze3.8s (13.2%)

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

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample238.0ms (0.8%)

Algorithm

1×

intervals

Results

145.0ms	165×	body	1024	valid
28.0ms	16×	body	2048	valid
27.0ms	52×	body	512	valid
4.0ms	13×	body	256	valid
2.0ms	10×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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

15.5b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize26.0ms (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)))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite113.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

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:

6.0ms	(cos.f64 (-.f64 lambda1 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)) (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)

series796.0ms (2.8%)

Error

15.1b

Counts

4 → 46

Calls

4 calls:

371.0ms	(.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)
150.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
148.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
78.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2686 to 1636 computations (39.1% saved)

simplify99.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4756	2283
1	4756	2283

prune160.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	88	15	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	15	104

Error

3.8b

Counts

104 → 15

Compiler

Compiled 2919 to 645 computations (77.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite135.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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 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 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)

series1.1s (3.9%)

Error

3.8b

Counts

4 → 42

Calls

4 calls:

577.0ms	(.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)
226.0ms	(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))))))
153.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
113.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3776 to 1960 computations (48.1% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4713	2944
1	4713	2944

prune191.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	93	13	106
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	104	17	121

Error

3.7b

Counts

121 → 17

Compiler

Compiled 3959 to 797 computations (79.9% saved)

localize30.0ms (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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 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 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
2.3b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))

rewrite109.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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 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)) (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))))
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)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 2357 to 308 computations (86.9% saved)

series1.3s (4.5%)

Error

3.7b

Counts

4 → 42

Calls

4 calls:

576.0ms	(.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)
290.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
234.0ms	(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))))))))
139.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4008 to 2107 computations (47.4% saved)

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4864	2897
1	4864	2897

prune164.0ms (0.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	101	17	118

Error

3.7b

Counts

118 → 17

Compiler

Compiled 3853 to 742 computations (80.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (log.f64 (exp.f64 (acos.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)
0.4b	(exp.f64 (acos.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))))))))
1.0b	(log.f64 (exp.f64 (acos.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)))))))))
1.4b	(acos.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)))))))

rewrite124.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

Rules

12×	`add-sqr-sqrt_binary64_1464`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`exp-prod_binary64_1494`
8×	`pow1_binary64_1503` `log-pow_binary64_1531`
7×	`associate-l_binary64_1383`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`add-log-exp_binary64_1481`
3×	`acos-asin_binary64_1623` `log-prod_binary64_1528` `associate-r_binary64_1382`
2×	`exp-diff_binary64_1490`
1×	`log-div_binary64_1529` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (log.f64 (exp.f64 (acos.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)
2.0ms	(log.f64 (exp.f64 (acos.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)))))))))
2.0ms	(exp.f64 (acos.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))))))))
1.0ms	(acos.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 2764 to 221 computations (92% saved)

series4.5s (15.7%)

Error

3.7b

Counts

4 → 51

Calls

4 calls:

2.3s	(.f64 (log.f64 (exp.f64 (acos.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)
1.6s	(log.f64 (exp.f64 (acos.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)))))))))
373.0ms	(exp.f64 (acos.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))))))))
219.0ms	(acos.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 5202 to 2575 computations (50.5% saved)

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4866	4840
1	4866	4840

prune147.0ms (0.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	2	13	15
Picked	1	0	1
Done	1	0	1
Total	107	19	126

Error

3.7b

Counts

126 → 19

Compiler

Compiled 3764 to 197 computations (94.8% saved)

regimes4.3s (15.1%)

Accuracy

Total 0.4b remaining (10.1%)

Threshold costs 0.4b (10.1%)

Compiler

Compiled 57450 to 33286 computations (42.1% saved)

bsearch0.0ms (0%)

simplify33.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 128 to 92 computations (28.1% saved)

end0.0ms (0%)

sample10.8s (37.8%)

Algorithm

1×

intervals

Results

4.9s	5459×	body	1024	valid
842.0ms	1438×	body	512	valid
603.0ms	291×	body	2048	valid
178.0ms	488×	body	256	valid
56.0ms	324×	body	128	valid
1.0ms	1×	body	512	invalid

Compiler

Compiled 5308 to 3076 computations (42% saved)

Details

analyze3.8s (13.2%)

sample238.0ms (0.8%)

simplify10.0ms (0%)

prune4.0ms (0%)

localize26.0ms (0.1%)

rewrite113.0ms (0.4%)

series796.0ms (2.8%)

simplify99.0ms (0.3%)

prune160.0ms (0.6%)

localize30.0ms (0.1%)

rewrite135.0ms (0.5%)

series1.1s (3.9%)

simplify121.0ms (0.4%)

prune191.0ms (0.7%)

localize30.0ms (0.1%)

rewrite109.0ms (0.4%)

series1.3s (4.5%)

simplify140.0ms (0.5%)

prune164.0ms (0.6%)

localize30.0ms (0.1%)

rewrite124.0ms (0.4%)

series4.5s (15.7%)

simplify140.0ms (0.5%)

prune147.0ms (0.5%)

regimes4.3s (15.1%)

bsearch0.0ms (0%)

simplify33.0ms (0.1%)

end0.0ms (0%)

sample10.8s (37.8%)

Profiling