Details

analyze4.4s (15.4%)

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)

sample279.0ms (1%)

Algorithm

1×

intervals

Results

171.0ms	171×	body	1024	valid
31.0ms	52×	body	512	valid
24.0ms	7×	body	2048	valid
13.0ms	15×	body	256	valid
2.0ms	11×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune15.0ms (0.1%)

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

16.1b

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)
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite127.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

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:

7.0ms	(*.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)

series647.0ms (2.2%)

Error

15.7b

Counts

4 → 42

Calls

4 calls:

305.0ms	(.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)
124.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
90.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
64.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2426 to 1487 computations (38.7% saved)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4919	2189
1	4919	2189

prune141.0ms (0.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	88	11	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	11	100

Error

4.1b

Counts

100 → 11

Compiler

Compiled 2687 to 516 computations (80.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))))))

rewrite140.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

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)

series948.0ms (3.3%)

Error

4.1b

Counts

4 → 42

Calls

4 calls:

461.0ms	(.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)
218.0ms	(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))))))
125.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
92.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3776 to 1965 computations (48% saved)

simplify152.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4876	2944
1	4876	2944

prune181.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	92	14	106
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	101	16	117

Error

3.9b

Counts

117 → 16

Compiler

Compiled 3979 to 792 computations (80.1% saved)

localize28.0ms (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)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))))))))
4.4b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))

rewrite102.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

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)

series1.1s (3.9%)

Error

3.9b

Counts

4 → 42

Calls

4 calls:

463.0ms	(.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)
345.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
179.0ms	(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))))))))
101.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3998 to 2108 computations (47.3% saved)

simplify162.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4871	2897
1	4871	2897

prune188.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	102	15	117

Error

3.9b

Counts

117 → 15

Compiler

Compiled 3869 to 739 computations (80.9% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))))))))
0.5b	(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)))))))))
0.8b	(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)))))))

rewrite105.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

11×	`add-sqr-sqrt_binary64_1464`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `exp-prod_binary64_1494`
5×	`add-log-exp_binary64_1481`
4×	`log-pow_binary64_1531`
3×	`acos-asin_binary64_1623` `log-prod_binary64_1528` `associate-l_binary64_1383` `associate-r_binary64_1382`
2×	`exp-diff_binary64_1490`
1×	`log-div_binary64_1529` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `sin-mult_binary64_1597` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 55

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(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 2349 to 318 computations (86.5% saved)

series1.9s (6.7%)

Error

3.9b

Counts

4 → 42

Calls

4 calls:

1.3s	(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)))))))))
312.0ms	(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))))))))
216.0ms	(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)))))))
87.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4188 to 2143 computations (48.8% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4893	3410
1	4893	3410

prune128.0ms (0.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	94	18	112

Error

3.9b

Counts

112 → 18

Compiler

Compiled 3265 to 296 computations (90.9% saved)

regimes4.4s (15.4%)

Accuracy

Total 0.4b remaining (10.1%)

Threshold costs 0.4b (10.1%)

Compiler

Compiled 53410 to 32080 computations (39.9% saved)

bsearch0.0ms (0%)

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	47
1	33	47

Remove

(sort phi1 phi2)

Compiler

Compiled 168 to 144 computations (14.3% saved)

end0.0ms (0%)

sample13.2s (45.7%)

Algorithm

1×

intervals

Results

6.1s	5547×	body	1024	valid
868.0ms	1374×	body	512	valid
491.0ms	220×	body	2048	valid
223.0ms	559×	body	256	valid
60.0ms	300×	body	128	valid
2.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 4923 to 2963 computations (39.8% saved)

Details

analyze4.4s (15.4%)

sample279.0ms (1%)

simplify11.0ms (0%)

prune15.0ms (0.1%)

localize19.0ms (0.1%)

rewrite127.0ms (0.4%)

series647.0ms (2.2%)

simplify104.0ms (0.4%)

prune141.0ms (0.5%)

localize25.0ms (0.1%)

rewrite140.0ms (0.5%)

series948.0ms (3.3%)

simplify152.0ms (0.5%)

prune181.0ms (0.6%)

localize28.0ms (0.1%)

rewrite102.0ms (0.4%)

series1.1s (3.9%)

simplify162.0ms (0.6%)

prune188.0ms (0.7%)

localize33.0ms (0.1%)

rewrite105.0ms (0.4%)

series1.9s (6.7%)

simplify121.0ms (0.4%)

prune128.0ms (0.4%)

regimes4.4s (15.4%)

bsearch0.0ms (0%)

simplify49.0ms (0.2%)

end0.0ms (0%)

sample13.2s (45.7%)

Profiling