Details

Time bar (total: 13.1s)

sample269.0ms

Algorithm
intervals
Results
194.0ms155×body1280valid
45.0ms68×body640valid
9.0ms20×body320valid
2.0ms8×body160valid
1.0ms5×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02712
13912
24412
34512
44512

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.5b

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)
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b
(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 72
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

series119.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin phi1) (sin phi2))
42.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms
(cos (- lambda1 lambda2))

simplify61.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0323995
1789819
22620818
35002793

prune356.0ms

Filtered
84 candidates to 58 candidates (69.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New661884
Fresh000
Picked101
Done000
Total671885

Merged error: 3.7b

Counts
85 → 18

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 80
Calls
4 calls:
10.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
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)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
46.0ms
(* (sin phi1) (sin phi2))
67.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05071394
122681185
250021184

prune535.0ms

Filtered
92 candidates to 66 candidates (71.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New781492
Fresh12517
Picked101
Done000
Total9119110

Merged error: 3.5b

Counts
110 → 19

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 66
Calls
4 calls:
5.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series147.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
42.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
16.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify121.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 4 (45.0ms)

IterNodesCost
01931705
14381457
210561453
314691453
437541449
550011449

prune452.0ms

Filtered
78 candidates to 53 candidates (67.9%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New69978
Fresh9918
Picked101
Done000
Total791897

Merged error: 3.5b

Counts
97 → 18

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(pow (* (sin phi1) (sin phi2)) 3)
1.0b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
28.6b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 75
Calls
4 calls:
3.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
5.0ms
(pow (* (sin phi1) (sin phi2)) 3)
2.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series193.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
64.0ms
(pow (* (sin phi1) (sin phi2)) 3)
16.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
43.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify42.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03001137
11071991
25001990

prune499.0ms

Filtered
87 candidates to 60 candidates (69.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New86187
Fresh01717
Picked101
Done000
Total8718105

Merged error: 3.5b

Counts
105 → 18

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03521
13521

end0.0ms

sample8.3s

Algorithm
intervals
Results
6.0s4785×body1280valid
1.5s2102×body640valid
325.0ms683×body320valid
86.0ms284×body160valid
27.0ms7×body2560valid
23.0ms141×body80valid