Details

Time bar (total: 9.9s)

sample63.0ms

Algorithm
intervals
Results
15.0ms255×body80valid
10.0ms38×body640valid
9.0ms23×body1280valid
5.0ms27×body320valid
1.0ms11×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.5b
(cos (/ (+ phi1 phi2) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))

series515.0ms

Counts
3 → 9
Calls
3 calls:
408.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
78.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify96.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0290525
11003448
24763442
35001440

prune219.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
2.5b
(cos (* 0.5 (+ phi2 phi1)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
12×distribute-rgt-in distribute-lft-in
8×associate-*r*
7×pow1 add-exp-log add-cbrt-cube
6×associate-*l*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg cos-sum associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 77
Calls
3 calls:
7.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
34.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
12.0ms
(cos (* 0.5 (+ phi2 phi1)))

series517.0ms

Counts
3 → 9
Calls
3 calls:
382.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
108.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
27.0ms
(cos (* 0.5 (+ phi2 phi1)))

simplify46.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0365925
11380736
25001723

prune227.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.2b
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
0.2b
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
19×prod-diff
11×distribute-rgt-in distribute-lft-in associate-*r*
10×pow1 add-exp-log add-cbrt-cube
9×flip3-- associate-*l* flip-- sin-mult
8×frac-times cos-mult
6×add-log-exp
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*r/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 117
Calls
4 calls:
7.0ms
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
52.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
27.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
165.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
89.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
58.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
453.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

simplify114.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08682669
140712372
250012360

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (- (pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3) (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)) (- lambda1 lambda2)) (+ (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5)))) (+ (* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))))
0.3b
(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
0.4b
(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
0.5b
(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

rewrite571.0ms

Algorithm
rewrite-expression-head
Rules
73×cos-mult
61×sin-mult
60×frac-add
49×pow1
38×frac-times
35×associate-/r/
34×associate-*l/
32×associate-*r/
27×add-exp-log add-cbrt-cube
19×pow-prod-down
14×cube-div associate-/l/
11×prod-exp cbrt-unprod
8×add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity flip--
6×pow-unpow
4×expm1-log1p-u pow-pow flip3-+ pow-exp pow-sqr pow-prod-up flip-+ log1p-expm1-u add-log-exp rem-cube-cbrt
3×times-frac associate-/r* frac-sub sub-div
2×cbrt-undiv cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod div-exp sqr-pow
1×pow2 frac-2neg swap-sqr associate-*r* associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 161
Calls
4 calls:
425.0ms
(/ (* (- (pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3) (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)) (- lambda1 lambda2)) (+ (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5)))) (+ (* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))))
18.0ms
(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
100.0ms
(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
17.0ms
(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

series1.5s

Counts
4 → 12
Calls
4 calls:
1.3s
(/ (* (- (pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3) (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)) (- lambda1 lambda2)) (+ (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5)))) (+ (* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))))
87.0ms
(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
66.0ms
(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
67.0ms
(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

simplify79.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
014645837
150015511

prune898.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes391.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04056
14056

end0.0ms

sample1.9s

Algorithm
intervals
Results
521.0ms8280×body80valid
366.0ms1269×body640valid
331.0ms808×body1280valid
148.0ms730×body320valid
50.0ms373×body160valid