Details

Time bar (total: 9.6s)

sample217.0ms

Algorithm
intervals
Results
140.0ms123×body1280valid
37.0ms59×body640valid
12.0ms27×body320valid
6.0ms21×body160valid
3.0ms26×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02012
12312
22312

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

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))))
4.0b
(sin (- lambda1 lambda2))
4.4b
(cos (- lambda1 lambda2))

rewrite28.0ms

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:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms
(sin (- lambda1 lambda2))
11.0ms
(cos (- lambda1 lambda2))

series148.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify72.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune327.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

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)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.4b
(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×cos-diff sub-neg fma-def associate-*r* associate-*l*
2×associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 76
Calls
4 calls:
11.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series267.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin 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))))
17.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04271128
11340942
25001940

prune473.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×fma-def
2×sub-neg associate-+r+ associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 76
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
48.0ms
(* (sin lambda1) (sin lambda2))
219.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03741090
11513949
25002941

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.5b
(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
0.6b
(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod fma-udef sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 79
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
2.0ms
(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
2.0ms
(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

series809.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin lambda1) (sin lambda2))
210.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
208.0ms
(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
341.0ms
(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

simplify40.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02561020
1923932
25002923

prune412.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes468.0ms

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
02722
12722

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.2s3539×body1280valid
1.2s2380×body640valid
303.0ms924×body320valid
97.0ms433×body160valid
72.0ms724×body80valid