Details

Time bar (total: 9.0s)

sample173.0ms

Algorithm
intervals
Results
102.0ms113×body1280valid
39.0ms69×body640valid
12.0ms35×body320valid
3.0ms13×body160valid
3.0ms26×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite30.0ms

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)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))
7.0ms
(sin (- lambda1 lambda2))

series147.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify71.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune310.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

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))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.6b
(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:
16.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
44.0ms
(* (sin lambda1) (sin lambda2))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms
(sin (- lambda1 lambda2))

simplify73.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0310819
1773667
22958665
35002641

prune379.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite12.0ms

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
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-neg distribute-rgt-neg-out fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
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)))))
6.0ms
(* (cos lambda1) (sin (- lambda2)))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series242.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(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)))))
54.0ms
(* (cos lambda1) (sin (- lambda2)))
44.0ms
(* (sin lambda1) (sin lambda2))
127.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify76.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0270717
1866623
23299622
35001622

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log-prod log-pow log1p-expm1-u
3×associate-*r* associate-*l* fma-udef
2×exp-sum
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log sin-mult unswap-sqr
Counts
4 → 63
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (sin lambda1) (sin lambda2))
162.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
129.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
128.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify54.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0198556
1560490
21900486
35001485

prune434.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes422.0ms

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
03526
13526

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.2s3559×body1280valid
1.2s2334×body640valid
336.0ms984×body320valid
95.0ms410×body160valid
75.0ms713×body80valid