Details

Time bar (total: 6.3s)

sample64.0ms

Algorithm
intervals
Results
18.0ms269×body80valid
12.0ms29×body1280valid
8.0ms29×body640valid
5.0ms27×body320valid
2.0ms12×body160valid

simplify55.0ms

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: 4.6b

localize17.0ms

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)))
3.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

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:
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series553.0ms

Counts
3 → 9
Calls
3 calls:
439.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
87.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify95.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0290525
11003448
24763442
35001440

prune227.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

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))
3.3b
(cos (* 0.5 (+ phi2 phi1)))

rewrite27.0ms

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:
3.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
17.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))

series554.0ms

Counts
3 → 9
Calls
3 calls:
404.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
123.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
26.0ms
(cos (* 0.5 (+ phi2 phi1)))

simplify45.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0365925
11380736
25001723

prune219.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
0.2b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (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))
0.2b
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite92.0ms

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* cos-mult flip-- sin-mult
8×frac-times
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 → 118
Calls
4 calls:
8.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
15.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
53.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
12.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
102.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
293.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
66.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify80.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06222233
126322015
250012014

prune728.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×associate-*l*
10×add-cube-cbrt *-un-lft-identity
8×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
2×unswap-sqr
Counts
4 → 80
Calls
4 calls:
6.0ms
(* lambda2 (sin (* 0.5 phi1)))
6.0ms
(* (cos (* 0.5 phi1)) lambda2)
13.0ms
(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
14.0ms
(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

series244.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* lambda2 (sin (* 0.5 phi1)))
48.0ms
(* (cos (* 0.5 phi1)) lambda2)
69.0ms
(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
84.0ms
(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

simplify37.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0281588
11179482
25001482

prune423.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes335.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03328
13328

end0.0ms

sample1.9s

Algorithm
intervals
Results
567.0ms8354×body80valid
363.0ms1239×body640valid
326.0ms784×body1280valid
167.0ms784×body320valid
48.0ms353×body160valid