Details

Time bar (total: 13.4s)

sample257.0ms

Algorithm
intervals
Results
186.0ms142×body1280valid
38.0ms56×body640valid
10.0ms23×body320valid
4.0ms24×body80valid
3.0ms11×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02715
14615
27115
37715
47715

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
15.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series191.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260456
11016389
24756389
35001389

prune326.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (cos lambda2))
0.1b
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b
(cos (- lambda1 lambda2))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×cos-diff
2×cos-sum sin-neg *-commutative distribute-rgt-neg-out sin-cos-mult
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ unsub-neg associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 63
Calls
4 calls:
4.0ms
(* (sin lambda1) (cos lambda2))
4.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
13.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))

series245.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin lambda1) (cos lambda2))
95.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
90.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0348545
11432476
25001475

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.2b
(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt *-un-lft-identity sin-mult
6×associate-*r* cos-mult
5×sin-cos-mult
4×frac-times associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sub-neg flip3-- sin-neg distribute-rgt-neg-out frac-sub flip-- sub-div
2×distribute-rgt-in distribute-lft-in *-commutative
1×+-commutative flip3-+ diff-log unsub-neg associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 78
Calls
4 calls:
5.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
5.0ms
(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
6.0ms
(* (sin lambda1) (sin (- lambda2)))
25.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
88.0ms
(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
57.0ms
(* (sin lambda1) (sin (- lambda2)))
182.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04661102
12150963
25001960

prune562.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
0.4b
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.4b
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.4b
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
26×cos-mult sin-mult
25×cbrt-prod
23×add-sqr-sqrt
16×frac-times
15×add-cube-cbrt *-un-lft-identity
13×flip3-- frac-sub flip-- sub-div
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×associate-*r/ associate-*l/ add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
39.0ms
(* (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
5.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
5.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
5.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series623.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(* (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
153.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
148.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
153.0ms
(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02892715
19942530
250022456

prune803.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes393.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05478
15478

end0.0ms

sample8.5s

Algorithm
intervals
Results
6.2s4669×body1280valid
1.6s1865×body640valid
288.0ms599×body320valid
92.0ms633×body80valid
68.0ms234×body160valid