Details

Time bar (total: 13.7s)

sample176.0ms

Algorithm
intervals
Results
101.0ms114×body1280valid
48.0ms83×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

prune3.0ms

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))

rewrite20.0ms

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:
7.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series198.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

simplify73.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune274.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize36.0ms

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))

series256.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (cos lambda1) (sin (- lambda2)))
84.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
101.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms
(cos (- lambda1 lambda2))

simplify122.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0309519
11110444
24851443
35001443

prune541.0ms

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)))))

rewrite22.0ms

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×associate-+r+ sin-neg unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+ sin-mult
Counts
4 → 70
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
6.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (cos lambda1) (sin (- lambda2)))
84.0ms
(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
44.0ms
(* (sin lambda1) (sin lambda2))
222.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0370662
11430564
25001563

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×add-sqr-sqrt add-cube-cbrt
15×times-frac frac-add cos-mult
14×associate-*r/
13×associate-/r/
10×add-exp-log add-cbrt-cube
8×pow1
6×frac-times pow-unpow flip3-+ flip-+ add-log-exp
5×flip3-- flip-- associate-/l*
4×unpow-prod-down cube-prod sum-cubes sin-mult distribute-lft-out
3×cube-div pow-pow associate-*l/ pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 associate--l+ associate-/l/ sqr-pow
1×cbrt-undiv distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-exp pow-prod-down prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 112
Calls
4 calls:
29.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
3.0ms
(pow (cos phi1) 3)
9.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
9.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series4.1s

Counts
4 → 12
Calls
4 calls:
3.7s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
28.0ms
(pow (cos phi1) 3)
189.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
214.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify54.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010824127
150013885

prune859.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes583.0ms

Accuracy

0% (0.1b 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
04854
15054
25054

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.2s3542×body1280valid
1.3s2445×body640valid
314.0ms937×body320valid
87.0ms395×body160valid
69.0ms681×body80valid