Details

Time bar (total: 10.0s)

sample174.0ms

Algorithm
intervals
Results
94.0ms112×body1280valid
41.0ms86×body640valid
16.0ms30×body320valid
3.0ms22×body80valid
1.0ms6×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize20.0ms

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))))
2.4b
(cos (- lambda1 lambda2))
2.4b
(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(cos (- lambda1 lambda2))
10.0ms
(sin (- lambda1 lambda2))

series141.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
92.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

simplify123.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33685374
45002374

prune235.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
2.4b
(sin (- lambda1 lambda2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×sin-sum
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 47
Calls
4 calls:
11.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
12.0ms
(sin (- lambda1 lambda2))

series191.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
112.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
19.0ms
(sin (- lambda1 lambda2))

simplify101.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0259561
1901490
23361489
35002489

prune308.0ms

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

rewrite80.0ms

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* add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 61
Calls
4 calls:
58.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
44.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
112.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0340888
11422774
25002773

prune359.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos phi1) 3)
0.4b
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
0.6b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
0.6b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×add-sqr-sqrt add-cube-cbrt
15×times-frac
13×add-exp-log add-cbrt-cube
11×pow1
9×cos-mult
7×associate-/r/
6×pow-unpow add-log-exp
5×associate-*l/ frac-add associate-/l*
4×unpow-prod-down pow-pow cube-prod pow-exp sum-cubes distribute-lft-out rem-cube-cbrt
3×flip3-- pow-prod-down prod-exp associate-/r* flip-- cbrt-unprod
2×cube-mult frac-times pow-to-exp flip3-+ unpow3 associate-*r/ flip-+ associate-/l/ sqr-pow
1×cbrt-undiv cube-div sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 105
Calls
4 calls:
3.0ms
(pow (cos phi1) 3)
225.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
22.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
28.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series886.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (cos phi1) 3)
635.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
105.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
120.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify142.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
06532406
136482203
250022198

prune643.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes590.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04666
14666

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3604×body1280valid
1.2s2319×body640valid
322.0ms984×body320valid
87.0ms411×body160valid
65.0ms682×body80valid