Details

Time bar (total: 7.6s)

sample63.0ms

Algorithm
intervals
Results
18.0ms269×body80valid
11.0ms37×body640valid
10.0ms23×body1280valid
5.0ms23×body320valid
1.0ms8×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.7b
(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series923.0ms

Counts
4 → 12
Calls
4 calls:
368.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
441.0ms
(* (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))

simplify42.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0328677
11130579
25001569

prune278.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
4.7b
(cos (* 0.5 (+ phi2 phi1)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
12×distribute-rgt-in distribute-lft-in
8×pow1 add-exp-log associate-*r* add-cbrt-cube
6×associate-*l*
4×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×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
3.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
16.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.0ms
(cos (* 0.5 (+ phi2 phi1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
527.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
406.0ms
(* (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)))

simplify50.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03951071
11515866
25001851

prune273.0ms

Pruning

6 alts after pruning (6 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)))
0.1b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b
(* (- (* (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)))

rewrite80.0ms

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:
6.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
12.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
49.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
7.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
103.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
305.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
62.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify82.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06222233
126322015
250012014

prune534.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))))
0.1b
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))) (- lambda1 lambda2))
0.2b
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt prod-diff
11×distribute-rgt-in distribute-lft-in
8×pow1 add-exp-log associate-*r* add-cbrt-cube
7×flip3-- flip--
6×associate-*l* add-log-exp
5×expm1-log1p-u
4×frac-times log1p-expm1-u
3×sub-neg
2×associate-*r/ pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef fma-neg diff-log log1p-expm1 sin-mult distribute-lft-out-- expm1-udef associate--r- difference-of-squares
Counts
4 → 103
Calls
4 calls:
0.0ms
(log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
7.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))))
31.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))) (- lambda1 lambda2))
7.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series672.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
141.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))))
347.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (expm1 (log1p (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))) (- lambda1 lambda2))
67.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify78.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05782307
123191897
250011891

prune466.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes290.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03235
13235

end0.0ms

sample1.9s

Algorithm
intervals
Results
587.0ms8316×body80valid
387.0ms1252×body640valid
364.0ms828×body1280valid
157.0ms722×body320valid
51.0ms358×body160valid