Details

Time bar (total: 9.1s)

sample176.0ms

Algorithm
intervals
Results
105.0ms111×body1280valid
44.0ms86×body640valid
9.0ms27×body320valid
2.0ms23×body80valid
2.0ms9×body160valid

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: 0.7b

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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite23.0ms

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
(sin (- lambda1 lambda2))
7.0ms
(cos (- lambda1 lambda2))

series154.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
23.0ms
(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune329.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×cos-diff
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log cos-mult *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 71
Calls
4 calls:
6.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos phi2) (cos (- lambda1 lambda2)))
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))

simplify92.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0368908
1989753
23930750
35001749

prune424.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×associate-*l/ fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
9.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
4.0ms
(* (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)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series266.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
45.0ms
(* (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)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify106.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0226727
1898621
24339620
35002620

prune410.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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)))
0.4b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite8.0ms

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))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
164.0ms
(exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
125.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
125.0ms
(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify52.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0198556
1560490
21900486
35001485

prune397.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes480.0ms

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

sample5.3s

Algorithm
intervals
Results
3.3s3551×body1280valid
1.3s2449×body640valid
321.0ms943×body320valid
87.0ms372×body160valid
69.0ms685×body80valid