Details

Time bar (total: 26.8s)

analyze3.8s (14.3%)

Algorithm
search
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02392341
12392341
055
155
Search
TrueOtherFalseIter
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)

sample258.0ms (1%)

Algorithm
intervals
Results
171.0ms189×body1024valid
22.0ms43×body512valid
21.0msbody2048valid
3.0msbody256valid
1.0msbody128valid
Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify12.0ms (0%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
09631
19631

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.0b
Counts
2 → 1
Compiler

Compiled 38 to 34 computations (10.5% saved)

localize18.0ms (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)
0.9b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.9b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite109.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
11×pow1_binary64_1844 add-exp-log_binary64_1821 add-cbrt-cube_binary64_1819
10×add-sqr-sqrt_binary64_1805
add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
associate-*r*_binary64_1723
cos-sum_binary64_1917 add-log-exp_binary64_1822 pow-prod-down_binary64_1854 prod-exp_binary64_1832 cbrt-unprod_binary64_1816 associate-*l*_binary64_1724
cos-diff_binary64_1920 cancel-sign-sub-inv_binary64_1749
*-commutative_binary64_1714
sub-neg_binary64_1776 acos-asin_binary64_1964 unswap-sqr_binary64_1751 distribute-rgt-in_binary64_1733 distribute-lft-in_binary64_1732 cos-mult_binary64_1937 associate-*l/_binary64_1726
Counts
4 → 59
Calls

4 calls:

13.0ms
(*.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)))))
Compiler

Compiled 1775 to 321 computations (81.9% saved)

series846.0ms (3.2%)

Error
13.2b
Counts
4 → 60
Calls

4 calls:

402.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
240.0ms
(*.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)
92.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
55.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3723 to 2134 computations (42.7% saved)

simplify83.0ms (0.3%)

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
051872925

prune143.0ms (0.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10415119
Fresh000
Picked101
Done000
Total10515120
Error
3.2b
Counts
120 → 15
Compiler

Compiled 3332 to 720 computations (78.4% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.9b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite132.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
3.1b
Rules
20×pow1_binary64_1844 add-exp-log_binary64_1821 add-cbrt-cube_binary64_1819
12×add-sqr-sqrt_binary64_1805
10×pow-prod-down_binary64_1854 prod-exp_binary64_1832 cbrt-unprod_binary64_1816
add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
associate-*l*_binary64_1724 associate-*r*_binary64_1723
add-log-exp_binary64_1822
*-commutative_binary64_1714 sin-mult_binary64_1938
unswap-sqr_binary64_1751 cos-mult_binary64_1937
acos-asin_binary64_1964 frac-times_binary64_1793 associate-*l/_binary64_1726 associate-*r/_binary64_1725
Counts
4 → 70
Calls

4 calls:

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

Compiled 3146 to 420 computations (86.6% saved)

series1.1s (4.2%)

Error
3.2b
Counts
4 → 51
Calls

4 calls:

444.0ms
(*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
371.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
163.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
100.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 4942 to 2434 computations (50.7% saved)

simplify102.0ms (0.4%)

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049373500
149373500

prune163.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New11011121
Fresh10414
Picked101
Done000
Total12115136
Error
3.1b
Counts
136 → 15
Compiler

Compiled 4808 to 873 computations (81.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.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))))))))
0.7b
(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)))))))))
0.9b
(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)))))))

rewrite110.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
3.1b
Rules
12×add-sqr-sqrt_binary64_1805
10×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
exp-prod_binary64_1835
pow1_binary64_1844 log-pow_binary64_1872
associate-*l*_binary64_1724
add-exp-log_binary64_1821 add-cbrt-cube_binary64_1819
add-log-exp_binary64_1822
acos-asin_binary64_1964 log-prod_binary64_1869 associate-*r*_binary64_1723
exp-diff_binary64_1831
log-div_binary64_1870 rem-log-exp_binary64_1824 rem-exp-log_binary64_1823 pow-prod-down_binary64_1854 prod-exp_binary64_1832 cbrt-unprod_binary64_1816 unswap-sqr_binary64_1751 *-commutative_binary64_1714
Counts
4 → 58
Calls

4 calls:

5.0ms
(*.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)
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 2764 to 221 computations (92% saved)

series3.1s (11.4%)

Error
3.1b
Counts
4 → 51
Calls

4 calls:

1.5s
(*.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)
1.1s
(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)))))))))
265.0ms
(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))))))))
167.0ms
(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)

simplify143.0ms (0.5%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
048664840
148664840

prune146.0ms (0.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1018109
Fresh6814
Picked101
Done000
Total10816124
Error
3.1b
Counts
124 → 16
Compiler

Compiled 4600 to 601 computations (86.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
0.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))))) R)
0.9b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
30.0b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))

rewrite136.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
3.1b
Rules
16×pow1_binary64_1844 add-exp-log_binary64_1821 add-cbrt-cube_binary64_1819
10×add-sqr-sqrt_binary64_1805
add-cube-cbrt_binary64_1818 cbrt-prod_binary64_1814 *-un-lft-identity_binary64_1783
pow-prod-down_binary64_1854 prod-exp_binary64_1832 cbrt-unprod_binary64_1816
add-log-exp_binary64_1822 associate-*r/_binary64_1725 pow-pow_binary64_1855 pow-exp_binary64_1851 rem-cube-cbrt_binary64_1806
associate-*l*_binary64_1724 associate-*r*_binary64_1723 pow-unpow_binary64_1860
cos-mult_binary64_1937 cube-div_binary64_1812 unpow-prod-down_binary64_1862 unpow3_binary64_1849 cube-mult_binary64_1813 cube-prod_binary64_1811 sqr-pow_binary64_1755
pow1/3_binary64_1865 cbrt-div_binary64_1815 rem-cbrt-cube_binary64_1807 acos-asin_binary64_1964 unswap-sqr_binary64_1751 *-commutative_binary64_1714 pow-to-exp_binary64_1852
Counts
4 → 73
Calls

4 calls:

10.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
5.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))
3.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))))) R)
1.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
Compiler

Compiled 3679 to 870 computations (76.4% saved)

series1.8s (6.7%)

Error
3.1b
Counts
4 → 57
Calls

4 calls:

760.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)
423.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))
371.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))))) R)
160.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3)))))
Compiler

Compiled 6055 to 3291 computations (45.6% saved)

simplify100.0ms (0.4%)

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
052494145

prune139.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1300130
Fresh01515
Picked011
Done000
Total13016146
Error
3.1b
Counts
146 → 16
Compiler

Compiled 4871 to 812 computations (83.3% saved)

regimes3.5s (13.2%)

Accuracy

Total 0.4b remaining (10.6%)

Threshold costs 0.4b (10.6%)

Compiler

Compiled 57278 to 31350 computations (45.3% saved)

bsearch0.0ms (0%)

simplify45.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03557
13557
Remove

(sort phi1 phi2)

Compiler

Compiled 204 to 150 computations (26.5% saved)

end0.0ms (0%)

sample10.7s (39.8%)

Algorithm
intervals
Results
4.8s5545×body1024valid
810.0ms1388×body512valid
541.0ms264×body2048valid
179.0ms501×body256valid
51.0ms302×body128valid
1.0msbody1024invalid
Compiler

Compiled 5290 to 2885 computations (45.5% saved)

Profiling

Loading profile data...