Details

Time bar (total: 11.6s)

sample276.0ms

Algorithm
intervals
Results
206.0ms169×body1280valid
37.0ms57×body640valid
8.0ms18×body320valid
3.0ms10×body160valid
0.0ms2×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune5.0ms

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: 18.3b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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)))))
4.0b
(cos (- lambda1 lambda2))

rewrite15.0ms

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×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
6.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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)))))
4.0ms
(cos (- lambda1 lambda2))

series64.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
7.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

simplify103.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264773
11022655
24705655
35002655

prune153.0ms

Filtered
69 candidates to 49 candidates (29.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New571269
Fresh000
Picked101
Done000
Total581270

Merged error: 3.6b

Counts
70 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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×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 → 72
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
10.0ms
(* (* (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))))))

series110.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin lambda1) (sin lambda2))
41.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
48.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify69.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04731301
121441096
250021095

prune182.0ms

Filtered
84 candidates to 55 candidates (34.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New721284
Fresh10111
Picked101
Done000
Total831396

Merged error: 3.5b

Counts
96 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.5b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r*
5×add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×log-prod log-pow cos-mult
2×frac-times flip3-+ associate-*r/ *-commutative flip-+
1×distribute-rgt-in acos-asin exp-prod exp-to-pow distribute-lft-in rem-log-exp associate-*l/ unswap-sqr
Counts
4 → 65
Calls
4 calls:
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
10.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
60.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
9.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify53.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04021385
117801150
250011145

prune160.0ms

Filtered
77 candidates to 53 candidates (31.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New75277
Fresh11112
Picked101
Done000
Total771390

Merged error: 3.5b

Counts
90 → 13

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
0.4b
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b
(pow (* (cos lambda1) (cos lambda2)) 3)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
22×add-exp-log add-cbrt-cube
19×pow-prod-down
10×prod-exp cbrt-unprod
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
5×cos-mult
4×pow-pow pow-exp pow-sqr pow-prod-up add-log-exp rem-cube-cbrt
2×cube-div cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod sqr-pow
1×pow2 acos-asin frac-times associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ *-commutative sin-mult
Counts
4 → 91
Calls
4 calls:
5.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
13.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
7.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
14.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)
53.0ms
(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
04761061
12205950
25001950

prune129.0ms

Filtered
103 candidates to 56 candidates (45.6%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1030103
Fresh01212
Picked011
Done000
Total10313116

Merged error: 3.5b

Counts
116 → 13

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04143
14143

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.8s4788×body1280valid
1.5s2066×body640valid
329.0ms693×body320valid
93.0ms297×body160valid
32.0ms9×body2560valid
25.0ms148×body80valid

Profiling

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