Details

Time bar (total: 8.6s)

sample71.0ms

Algorithm
intervals
Results
17.0ms35×body1280valid
17.0ms257×body80valid
12.0ms41×body640valid
4.0ms20×body320valid
2.0ms14×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.0b

localize14.0ms

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)))
1.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

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)
10.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series926.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
443.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0328677
11130579
25001569

prune265.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

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))
1.6b
(cos (* 0.5 (+ phi2 phi1)))

rewrite26.0ms

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))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
506.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
409.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
119.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
30.0ms
(cos (* 0.5 (+ phi2 phi1)))

simplify54.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03951071
11515866
25001851

prune266.0ms

Pruning

8 alts after pruning (8 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
(* (- (* (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)))

rewrite73.0ms

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:
3.0ms
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
13.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
46.0ms
(* (- (* (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)))

series1.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
102.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
287.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
65.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify114.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08682672
140712375
250022363

prune549.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin (* 0.5 phi2)) 2)
0.2b
(fma (- lambda1 lambda2) (* (pow (cos (* 0.5 phi2)) 2) (pow (cos (* 0.5 phi1)) 2)) (* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2))))
0.3b
(pow (cos (* 0.5 phi2)) 2)
9.4b
(* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt add-cbrt-cube
8×pow1
7×prod-exp
6×unpow-prod-down pow-unpow
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-exp cbrt-unprod
2×pow-pow associate-*l/ unpow2 sqr-pow
1×distribute-lft-neg-out flip3-- associate-*r* pow-prod-down *-commutative distribute-rgt-neg-out flip-- fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
2.0ms
(pow (sin (* 0.5 phi2)) 2)
0.0ms
(fma (- lambda1 lambda2) (* (pow (cos (* 0.5 phi2)) 2) (pow (cos (* 0.5 phi1)) 2)) (* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2))))
2.0ms
(pow (cos (* 0.5 phi2)) 2)
34.0ms
(* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (sin (* 0.5 phi2)) 2)
291.0ms
(fma (- lambda1 lambda2) (* (pow (cos (* 0.5 phi2)) 2) (pow (cos (* 0.5 phi1)) 2)) (* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2))))
31.0ms
(pow (cos (* 0.5 phi2)) 2)
141.0ms
(* (- lambda1 lambda2) (* (- (pow (sin (* 0.5 phi2)) 2)) (pow (sin (* 0.5 phi1)) 2)))

simplify60.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0450891
11771761
25002745

prune561.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes410.0ms

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
04534
15334
25734
35734

end0.0ms

sample1.9s

Algorithm
intervals
Results
542.0ms8313×body80valid
375.0ms1266×body640valid
375.0ms862×body1280valid
149.0ms726×body320valid
54.0ms373×body160valid