Details

Time bar (total: 12.5s)

sample261.0ms

Algorithm
intervals
Results
190.0ms158×body1280valid
39.0ms58×body640valid
11.0ms23×body320valid
3.0ms10×body160valid
1.0ms7×body80valid

simplify7.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.1b

Counts
2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.3b
(* (sin phi1) (sin phi2))
0.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b
(cos (- lambda1 lambda2))

rewrite15.0ms

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:
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
5.0ms
(* (sin phi1) (sin phi2))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms
(cos (- lambda1 lambda2))

series117.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
47.0ms
(* (sin phi1) (sin phi2))
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune281.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New541367
Fresh000
Picked101
Done000
Total551368

Merged error: 2.6b

Counts
68 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(* (sin phi1) (sin phi2))
0.6b
(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×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:
10.0ms
(* (* (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))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
68.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
42.0ms
(* (sin phi1) (sin phi2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04861308
121651096
250011095

prune409.0ms

Filtered
84 candidates to 56 candidates (66.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New701484
Fresh10212
Picked101
Done000
Total811697

Merged error: 2.5b

Counts
97 → 16

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin phi2))
0.3b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×log-pow
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 55
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
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))))))

series122.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin phi1) (sin phi2))
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))))))

simplify79.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01841090
1449921
2899921
31236921
42522921
55001921

prune375.0ms

Filtered
67 candidates to 43 candidates (64.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New61667
Fresh41115
Picked101
Done000
Total661783

Merged error: 2.4b

Counts
83 → 17

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(cbrt (sin phi1))
0.6b
(acos (+ (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin phi2))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
1×acos-asin
Counts
4 → 41
Calls
4 calls:
2.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))
2.0ms
(cbrt (sin phi1))
1.0ms
(acos (+ (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin phi2))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(cbrt (sin phi1))
91.0ms
(cbrt (sin phi1))
99.0ms
(cbrt (sin phi1))
16.0ms
(acos (+ (* (* (cbrt (sin phi1)) (cbrt (sin phi1))) (* (cbrt (sin phi1)) (sin phi2))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0140507
1318445
2698439
31650436
45001436

prune294.0ms

Filtered
53 candidates to 42 candidates (79.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New52153
Fresh01616
Picked101
Done000
Total531770

Merged error: 2.4b

Counts
70 → 17

regimes1.3s

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
03419
13419

end0.0ms

sample8.3s

Algorithm
intervals
Results
6.0s4804×body1280valid
1.5s2100×body640valid
308.0ms682×body320valid
86.0ms265×body160valid
35.0ms11×body2560valid
23.0ms141×body80valid

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