Details

Time bar (total: 12.4s)

sample270.0ms

Algorithm
intervals
Results
198.0ms163×body1280valid
46.0ms67×body640valid
7.0ms16×body320valid
2.0ms6×body160valid
1.0ms4×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02712
13912
24412
34512
44512

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize25.0ms

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)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b
(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×*-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
12.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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)))))
8.0ms
(cos (- lambda1 lambda2))

series180.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
23.0ms
(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03881113
11250911
25001909

prune384.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
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)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite36.0ms

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* cos-mult
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative
2×sub-neg flip3-- prod-diff frac-sub flip-- sub-div unswap-sqr
1×acos-asin associate-*l/
Counts
4 → 86
Calls
4 calls:
4.0ms
(* (sin phi1) (sin phi2))
26.0ms
(* (* (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)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin phi1) (sin phi2))
215.0ms
(* (* (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)
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05251615
121801377
250021374

prune559.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity cos-mult
5×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×frac-times associate-*r/ associate-*l/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 84
Calls
4 calls:
15.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
126.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04341553
117161275
250021274

prune483.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.0b

localize38.0ms

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)
0.8b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
26.2b
(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×expm1-log1p-u log1p-expm1-u 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 → 75
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))

series209.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
69.0ms
(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)))))))
50.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify42.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03091181
110761041
250011028

prune457.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.0b

regimes555.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03320
13320

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.8s4817×body1280valid
1.6s2045×body640valid
327.0ms711×body320valid
86.0ms282×body160valid
22.0ms142×body80valid
21.0ms7×body2560valid