Details

Time bar (total: 12.0s)

sample311.0ms

Algorithm
intervals
Results
210.0ms150×body1280valid
56.0ms67×body640valid
12.0ms24×body320valid
4.0ms11×body160valid
1.0ms4×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
09519
19519

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 19.0b

Counts
2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.4b
(cos (- lambda1 lambda2))

rewrite16.0ms

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)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms
(cos (- lambda1 lambda2))

series58.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(* (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)))))
4.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049881033
149881033

prune167.0ms

Filtered
48 candidates to 69 candidates (-43.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New531669
Fresh000
Picked101
Done000
Total541670

Merged error: 4.9b

Counts
70 → 16

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
0.2b
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1 add-exp-log add-cbrt-cube
13×pow-prod-down prod-exp cbrt-unprod
10×add-sqr-sqrt
9×associate-*l*
8×add-cube-cbrt *-un-lft-identity
5×associate-*r*
4×associate-*r/ add-log-exp
3×*-commutative
2×cos-mult
1×acos-asin unswap-sqr
Counts
4 → 70
Calls
4 calls:
8.0ms
(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
9.0ms
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

series107.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
24.0ms
(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))))) R)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
052681473

prune186.0ms

Filtered
53 candidates to 82 candidates (-54.7%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New701282
Fresh12315
Picked101
Done000
Total831598

Merged error: 4.8b

Counts
98 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
1.0b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

rewrite12.0ms

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
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 → 58
Calls
4 calls:
5.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))) R)
2.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
2.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

series93.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))) R)
26.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))))
14.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))))
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049791928
149791928

prune172.0ms

Filtered
42 candidates to 70 candidates (-66.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh5914
Picked101
Done000
Total691685

Merged error: 4.8b

Counts
85 → 16

localize38.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1)))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))))))
9.0b
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
9.0b
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
9.0b
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3
1×acos-asin
Counts
4 → 35
Calls
4 calls:
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1)))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))))))
6.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
6.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
6.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))

series175.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1)))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))) (cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))))))
53.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
52.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))
56.0ms
(cbrt (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))

simplify59.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
05071775

prune57.0ms

Filtered
39 candidates to 47 candidates (-20.5%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New47047
Fresh01515
Picked011
Done000
Total471663

Merged error: 4.8b

Counts
63 → 16

regimes1.1s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03859
13859

end0.0ms

sample9.1s

Algorithm
intervals
Results
6.5s4830×body1280valid
1.6s2029×body640valid
370.0ms726×body320valid
95.0ms267×body160valid
31.0ms8×body2560valid
24.0ms141×body80valid

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