Details

Time bar (total: 10.6s)

sample177.0ms

Algorithm
intervals
Results
105.0ms114×body1280valid
43.0ms83×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
12112
22112

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize22.0ms

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))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
8.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series196.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify75.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune331.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×cos-diff distribute-rgt-neg-out
2×cos-sum associate-+r+ sin-neg *-commutative
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ sum-log flip-+ unswap-sqr
Counts
4 → 61
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
6.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series247.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos lambda1) (sin (- lambda2)))
81.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify119.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0309519
11110444
24851443
35001443

prune502.0ms

Filtered
73 candidates to 58 candidates (79.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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))
0.4b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*l*
7×associate-*r*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
3×*-commutative distribute-rgt-neg-out
2×sin-neg unswap-sqr
1×+-commutative flip3-+ sum-log flip-+ sin-mult
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
7.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (cos lambda1) (sin (- lambda2)))
85.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
44.0ms
(* (sin lambda1) (sin lambda2))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0340568
11432482
25001481

prune548.0ms

Filtered
80 candidates to 61 candidates (76.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (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))))
0.4b
(pow (cos phi1) 3)
0.7b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
1.3b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite51.0ms

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:
31.0ms
(/ (+ (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))))
3.0ms
(pow (cos phi1) 3)
7.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
7.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series971.0ms

Counts
4 → 12
Calls
4 calls:
688.0ms
(/ (+ (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))))
32.0ms
(pow (cos phi1) 3)
116.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
135.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify134.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
06532406
136482203
250022199

prune862.0ms

Filtered
117 candidates to 80 candidates (68.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes619.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05481
15481

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3542×body1280valid
1.3s2445×body640valid
316.0ms937×body320valid
99.0ms395×body160valid
68.0ms681×body80valid