Details

Time bar (total: 13.5s)

sample293.0ms

Algorithm
intervals
Results
212.0ms154×body1280valid
49.0ms57×body640valid
9.0ms16×body320valid
5.0ms23×body80valid
2.0ms6×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02815
14815
27915
39415
49415

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b
(cos (- lambda1 lambda2))
2.9b
(sin (- lambda1 lambda2))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×prod-diff
11×pow1 add-exp-log cos-sum sin-sum add-cbrt-cube
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×sub-neg *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 86
Calls
4 calls:
4.0ms
(* (sin phi1) (cos phi2))
13.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms
(cos (- lambda1 lambda2))
7.0ms
(sin (- lambda1 lambda2))

series167.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin phi1) (cos phi2))
86.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify42.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04111009
11289778
25001776

prune391.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b
(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow1 add-exp-log add-cbrt-cube
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-diff *-commutative
2×sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/
Counts
4 → 85
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
4.0ms
(* (sin phi1) (cos phi2))
12.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))

series188.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos phi1) (sin phi2))
40.0ms
(* (sin phi1) (cos phi2))
85.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0425787
11480631
25001628

prune497.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
5×sin-cos-mult
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 96
Calls
4 calls:
4.0ms
(* (sin phi1) (cos phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
14.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sin phi1) (cos phi2))
45.0ms
(* (sin lambda1) (sin lambda2))
94.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
109.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify56.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0397830
11810652
25001652

prune552.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp sin-cos-mult cbrt-unprod
5×sin-mult
4×expm1-log1p-u frac-times associate-*r/ cos-mult *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×sub-neg flip3-- prod-diff frac-sub flip-- sub-div
1×associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 98
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
4.0ms
(* (sin phi1) (cos phi2))
8.0ms
(* (sin lambda1) (sin (- lambda2)))
26.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos phi1) (sin phi2))
44.0ms
(* (sin phi1) (cos phi2))
51.0ms
(* (sin lambda1) (sin (- lambda2)))
177.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05151025
12339898
25003897

prune571.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes415.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04032
14032

end0.0ms

sample9.3s

Algorithm
intervals
Results
6.5s4583×body1280valid
1.9s1954×body640valid
354.0ms585×body320valid
167.0ms658×body80valid
81.0ms220×body160valid