Details

Time bar (total: 12.2s)

sample250.0ms

Algorithm
intervals
Results
174.0ms157×body1280valid
40.0ms65×body640valid
6.0ms16×body320valid
6.0ms1×body2560valid
3.0ms12×body160valid
1.0ms5×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize32.0ms

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)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b
(cos (- lambda1 lambda2))

rewrite33.0ms

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:
12.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (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)))))
11.0ms
(cos (- lambda1 lambda2))

series129.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
50.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
20.0ms
(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune303.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))))))

rewrite36.0ms

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×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
50.0ms
(* (sin phi1) (sin phi2))
73.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774

prune394.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
25.0b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite26.0ms

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×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 → 67
Calls
4 calls:
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
11.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
5.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series210.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
69.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
46.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify185.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
02851038
11031891
24820891
35001891

prune464.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.8b
(log (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))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
8×add-exp-log add-cbrt-cube
7×log-prod
6×associate-*r*
4×exp-sum add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×acos-asin rem-log-exp log-pow sin-mult
Counts
4 → 61
Calls
4 calls:
12.0ms
(* (sin phi1) (sin phi2))
18.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series190.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin phi1) (sin phi2))
74.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
53.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify189.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
02291302
16061089
213151074
319661072
444951072
550011072

prune370.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.0b

regimes935.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03421
13421

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.7s4735×body1280valid
1.4s2138×body640valid
306.0ms704×body320valid
81.0ms301×body160valid
17.0ms5×body2560valid
17.0ms119×body80valid