Details

Time bar (total: 9.4s)

sample216.0ms

Algorithm
intervals
Results
131.0ms114×body1280valid
53.0ms83×body640valid
10.0ms26×body320valid
3.0ms12×body160valid
3.0ms21×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(cos (- lambda1 lambda2))
2.6b
(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
33×add-sqr-sqrt sin-sum
31×add-cube-cbrt *-un-lft-identity
12×distribute-rgt-in distribute-lft-in
11×cos-sum
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 102
Calls
4 calls:
9.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
6.0ms
(sin (- lambda1 lambda2))

series196.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
25.0ms
(sin (- lambda1 lambda2))

simplify109.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
05051623
114301236
248731161
350011161

prune371.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×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* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cos-diff fma-def
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sub-neg sin-neg sum-log distribute-rgt-neg-out
Counts
4 → 84
Calls
4 calls:
9.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
5.0ms
(* (cos lambda1) (sin (- lambda2)))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(cos (- lambda1 lambda2))

series305.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
52.0ms
(* (cos lambda1) (sin (- lambda2)))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify54.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0513970
11956807
25001803

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite22.0ms

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×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ sin-neg distribute-rgt-neg-out flip-+ fma-udef sin-mult
Counts
4 → 76
Calls
4 calls:
9.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
5.0ms
(* (cos lambda1) (sin (- lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series492.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
48.0ms
(* (cos lambda1) (sin (- lambda2)))
46.0ms
(* (sin lambda1) (sin lambda2))
260.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify44.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0366688
11578609
25001606

prune515.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(log1p (* (cos lambda1) (sin (- lambda2))))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite13.0ms

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*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef log1p-expm1 sin-neg distribute-rgt-neg-out fma-udef sin-mult
Counts
4 → 63
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(log1p (* (cos lambda1) (sin (- lambda2))))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series293.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos lambda1) (sin (- lambda2)))
43.0ms
(* (sin lambda1) (sin lambda2))
76.0ms
(log1p (* (cos lambda1) (sin (- lambda2))))
122.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify68.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0245451
1787391
23022388
35001388

prune394.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes408.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3542×body1280valid
1.3s2445×body640valid
313.0ms937×body320valid
87.0ms395×body160valid
70.0ms681×body80valid