Details

Time bar (total: 11.9s)

sample271.0ms

Algorithm
intervals
Results
192.0ms159×body1280valid
46.0ms71×body640valid
9.0ms21×body320valid
5.0ms1×body2560valid
1.0ms4×body160valid

simplify6.0ms

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: 17.1b

localize24.0ms

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)
0.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
1.9b
(cos (- lambda1 lambda2))

rewrite14.0ms

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:
4.0ms
(* (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))

series119.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin phi1) (sin phi2))
48.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune341.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:
17.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms
(* (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))))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
48.0ms
(* (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))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04861308
121651097
250011096

prune454.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(pow (* (sin phi1) (sin phi2)) 3)
0.7b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
29.0b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite11.0ms

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:
3.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms
(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))))))
2.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series198.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
66.0ms
(pow (* (sin phi1) (sin phi2)) 3)
17.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
45.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify176.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02851038
11017891
24784891
35001891

prune460.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin phi2) 3)
0.4b
(pow (sin phi1) 3)
0.7b
(acos (+ (cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
29.0b
(cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log unpow-prod-down pow-unpow cube-prod add-cbrt-cube
4×add-log-exp
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×cbrt-prod acos-asin pow1/3 pow-prod-down rem-cbrt-cube
Counts
4 → 64
Calls
4 calls:
2.0ms
(pow (sin phi2) 3)
2.0ms
(pow (sin phi1) 3)
1.0ms
(acos (+ (cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3)))

series146.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin phi2) 3)
43.0ms
(pow (sin phi1) 3)
24.0ms
(acos (+ (cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
49.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin phi2) 3)))

simplify42.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0263521
1943455
25002445

prune345.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

regimes560.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03622
13622

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.7s4695×body1280valid
1.7s2179×body640valid
335.0ms698×body320valid
83.0ms286×body160valid
49.0ms15×body2560valid
20.0ms129×body80valid