Details

Time bar (total: 13.0s)

sample272.0ms

Algorithm
intervals
Results
195.0ms160×body1280valid
51.0ms67×body640valid
5.0ms11×body320valid
3.0ms10×body160valid
1.0ms8×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: 15.2b

Counts
2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (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)))))
3.8b
(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))

series121.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (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))

simplify65.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0323995
1789819
22620818
35002793

prune361.0ms

Filtered
84 candidates to 58 candidates (69.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New681684
Fresh000
Picked101
Done000
Total691685

Merged error: 3.7b

Counts
85 → 16

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 72
Calls
4 calls:
5.0ms
(* (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))))))

series175.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
43.0ms
(* (sin phi1) (sin phi2))
69.0ms
(* (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))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
02741015
1872860
22115860
33356860
45001860

prune456.0ms

Filtered
84 candidates to 59 candidates (70.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New731184
Fresh8715
Picked101
Done000
Total8218100

Merged error: 3.6b

Counts
100 → 18

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin lambda2))
0.6b
(cbrt (sin lambda2))
0.6b
(cbrt (sin lambda2))
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (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 expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×acos-asin
Counts
4 → 49
Calls
4 calls:
2.0ms
(cbrt (sin lambda2))
2.0ms
(cbrt (sin lambda2))
2.0ms
(cbrt (sin lambda2))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (sin lambda2))
99.0ms
(cbrt (sin lambda2))
103.0ms
(cbrt (sin lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
0149573
1362511
21063505
33458502
45001502

prune430.0ms

Filtered
61 candidates to 50 candidates (82.0%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New60161
Fresh11617
Picked011
Done000
Total611879

Merged error: 3.6b

Counts
79 → 18

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(pow (* (sin phi1) (sin phi2)) 3)
1.1b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
23.8b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite17.0ms

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* sin-mult
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 76
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
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))

series185.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin phi1) (sin phi2))
66.0ms
(pow (* (sin phi1) (sin phi2)) 3)
23.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
46.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0280658
11038602
25002600

prune412.0ms

Filtered
88 candidates to 62 candidates (70.5%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New86288
Fresh21416
Picked101
Done011
Total8917106

Merged error: 3.6b

Counts
106 → 17

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03424
13424

end0.0ms

sample8.3s

Algorithm
intervals
Results
6.0s4718×body1280valid
1.6s2145×body640valid
325.0ms681×body320valid
90.0ms298×body160valid
38.0ms13×body2560valid
34.0ms148×body80valid

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