Details

Time bar (total: 12.1s)

sample253.0ms

Algorithm
intervals
Results
170.0ms149×body1280valid
49.0ms69×body640valid
9.0ms22×body320valid
4.0ms1×body2560valid
2.0ms9×body160valid
1.0ms6×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.9b

Counts
2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.2b
(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
9.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms
(cos (- lambda1 lambda2))

series122.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin phi1) (sin phi2))
44.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21775569
35001569

prune261.0ms

Filtered
67 candidates to 49 candidates (26.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New501767
Fresh000
Picked101
Done000
Total511768

Merged error: 2.9b

Counts
68 → 17

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin phi1) (sin phi2))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×associate-*l*
23×add-sqr-sqrt
20×*-un-lft-identity
16×associate-*r*
13×pow1 add-exp-log add-cbrt-cube
12×add-cube-cbrt
6×cos-mult unswap-sqr
5×pow-prod-down prod-exp cbrt-unprod
4×*-commutative distribute-lft-out add-log-exp
3×frac-times associate-*r/ sin-mult
2×+-commutative distribute-rgt-in distribute-lft-in flip3-+ frac-add flip-+
1×acos-asin associate-*l/
Counts
4 → 91
Calls
4 calls:
24.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
5.0ms
(* (sin phi1) (sin phi2))
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
70.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
46.0ms
(* (sin phi1) (sin phi2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05611523
123951312
250021311

prune451.0ms

Filtered
103 candidates to 68 candidates (34.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New8617103
Fresh15116
Picked101
Done000
Total10218120

Merged error: 2.8b

Counts
120 → 18

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
0.2b
(* (sin phi1) (sin phi2))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
5.0ms
(* (sin phi1) (sin phi2))
3.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

series185.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (sin lambda1) (sin lambda2))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
47.0ms
(* (sin phi1) (sin phi2))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

simplify82.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0265963
1883808
22046808
33174808
45001808

prune384.0ms

Filtered
76 candidates to 51 candidates (32.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New69776
Fresh71017
Picked101
Done000
Total771794

Merged error: 2.8b

Counts
94 → 17

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
0.9b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log
6×exp-prod add-cbrt-cube
5×add-log-exp
4×log-pow
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff rem-log-exp
1×log-div pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
5.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
5.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
49.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
17.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) 1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

simplify98.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
01891136
1507969
21135969
31933969
43498969
55002969

prune272.0ms

Filtered
68 candidates to 44 candidates (35.3%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New61768
Fresh61016
Picked101
Done000
Total681785

Merged error: 2.7b

Counts
85 → 17

regimes912.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04143
14143

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.9s4735×body1280valid
1.5s2163×body640valid
331.0ms705×body320valid
80.0ms269×body160valid
20.0ms127×body80valid
16.0ms4×body2560valid