Details

Time bar (total: 10.3s)

sample200.0ms

Algorithm
intervals
Results
127.0ms122×body1280valid
42.0ms69×body640valid
10.0ms27×body320valid
4.0ms15×body160valid
3.0ms23×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b
(cos (- lambda1 lambda2))
2.8b
(sin (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(cos (- lambda1 lambda2))
7.0ms
(sin (- lambda1 lambda2))

series151.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
26.0ms
(sin (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune318.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.8b
(sin (- lambda1 lambda2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×sin-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×sub-neg pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
7.0ms
(sin (- lambda1 lambda2))

series207.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
43.0ms
(* (sin lambda1) (sin lambda2))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
20.0ms
(sin (- lambda1 lambda2))

simplify71.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0310819
1773667
22958665
35002641

prune370.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
3.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin 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)))))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series389.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin 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)))))
44.0ms
(* (sin lambda1) (sin lambda2))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify155.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0261833
1919744
24867738
35001738

prune413.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod fma-udef
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
1.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

series556.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
130.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
176.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

simplify180.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0170550
1633507
24294499
35001499

prune423.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes544.0ms

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
04059
14059

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.8s3647×body1280valid
1.4s2295×body640valid
383.0ms916×body320valid
115.0ms405×body160valid
94.0ms737×body80valid