Details

Time bar (total: 9.6s)

sample173.0ms

Algorithm
intervals
Results
104.0ms114×body1280valid
42.0ms83×body640valid
8.0ms26×body320valid
2.0ms12×body160valid
2.0ms21×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

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))
2.6b
(sin (- lambda1 lambda2))

rewrite34.0ms

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:
9.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series198.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
05051623
114301236
248731161
350011161

prune385.0ms

Filtered
114 candidates to 66 candidates (57.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
3×cos-diff fma-def distribute-rgt-neg-out
2×associate-+r+ sin-neg *-commutative
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ sum-log flip-+ unswap-sqr
Counts
4 → 81
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
6.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms
(cos (- lambda1 lambda2))

series258.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (cos lambda1) (sin (- lambda2)))
85.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
103.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0435833
11448663
25001661

prune510.0ms

Filtered
93 candidates to 71 candidates (76.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×pow1 add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
7×associate-*r*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×fma-def *-commutative distribute-rgt-neg-out
2×associate-+r+ sin-neg unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 81
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
7.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (cos lambda1) (sin (- lambda2)))
87.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
49.0ms
(* (sin lambda1) (sin lambda2))
225.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0387714
11516605
25001597

prune545.0ms

Filtered
93 candidates to 74 candidates (79.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos phi2) 3)
0.4b
(pow (cos phi1) 3)
0.6b
(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
1.3b
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×fma-udef
Counts
4 → 85
Calls
4 calls:
3.0ms
(pow (cos phi2) 3)
2.0ms
(pow (cos phi1) 3)
2.0ms
(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos phi2) 3)
29.0ms
(pow (cos phi1) 3)
110.0ms
(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
220.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

simplify46.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0320616
11404530
25001516

prune550.0ms

Filtered
97 candidates to 56 candidates (57.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes511.0ms

Accuracy

0% (0.1b 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
04251
14251

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3542×body1280valid
1.3s2445×body640valid
323.0ms937×body320valid
93.0ms395×body160valid
72.0ms681×body80valid