Details

Time bar (total: 9.7s)

sample183.0ms

Algorithm
intervals
Results
116.0ms124×body1280valid
36.0ms68×body640valid
10.0ms30×body320valid
5.0ms19×body160valid
2.0ms15×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: 0.8b

localize21.0ms

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))
2.8b
(sin (- lambda1 lambda2))

rewrite44.0ms

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:
15.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(cos (- lambda1 lambda2))
7.0ms
(sin (- lambda1 lambda2))

series191.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify108.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
05051623
114301236
248731161
350011161

prune372.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.8b
(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
33×sin-sum
30×add-sqr-sqrt
27×prod-diff
26×add-cube-cbrt *-un-lft-identity
11×distribute-rgt-in distribute-lft-in
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sub-neg
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-diff fma-udef sin-mult
Counts
4 → 94
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
15.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
7.0ms
(sin (- lambda1 lambda2))

series249.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
58.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
124.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
24.0ms
(sin (- lambda1 lambda2))

simplify91.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
04381341
113171038
24558964
35001964

prune451.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite23.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- fma-udef sin-mult
Counts
4 → 68
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series326.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin lambda1) (sin lambda2))
137.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify118.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0292936
11106822
24839821
35001821

prune440.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.4b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.5b
(cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3))
0.7b
(pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 67
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
1.0ms
(cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3))
1.0ms
(pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)

series449.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
130.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
123.0ms
(cbrt (pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3))
179.0ms
(pow (fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1)) 3)

simplify183.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0198998
1678909
24251898
35001898

prune352.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes448.0ms

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
03125
13125

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.4s3570×body1280valid
1.3s2344×body640valid
337.0ms907×body320valid
104.0ms427×body160valid
84.0ms752×body80valid