Details

Time bar (total: 10.0s)

sample82.0ms

Algorithm
intervals
Results
29.0ms264×body80valid
14.0ms30×body1280valid
12.0ms35×body640valid
6.0ms23×body320valid
2.0ms11×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

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)))
3.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

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)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series931.0ms

Counts
4 → 12
Calls
4 calls:
366.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
446.0ms
(* (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))

simplify38.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0328677
11130579
25001569

prune273.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

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))
3.2b
(cos (* 0.5 (+ phi2 phi1)))

rewrite27.0ms

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)
17.0ms
(* (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))
397.0ms
(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
118.0ms
(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
29.0ms
(cos (* 0.5 (+ phi2 phi1)))

simplify48.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03951071
11515866
25001851

prune259.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (- (* (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:
12.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
3.0ms
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
47.0ms
(* (- (* (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:
103.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
1.1s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
294.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
64.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify116.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08682669
140712372
250012360

prune584.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in associate-*r*
10×pow1 add-exp-log add-cbrt-cube
9×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sub-neg associate-*r/
1×flip3-- flip-- fma-udef sin-mult distribute-lft-out-- difference-of-squares
Counts
4 → 97
Calls
4 calls:
3.0ms
(* (hypot (* (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.0ms
(fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
15.0ms
(* (fma (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)))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (hypot (* (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- lambda1 lambda2)) (- phi1 phi2)) R)
105.0ms
(fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
311.0ms
(* (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- lambda1 lambda2))
61.0ms
(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify92.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06892152
131751858
250011851

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes355.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02818
12818

end0.0ms

sample2.3s

Algorithm
intervals
Results
889.0ms8419×body80valid
425.0ms1261×body640valid
379.0ms797×body1280valid
183.0ms725×body320valid
72.0ms363×body160valid