Details

Time bar (total: 27.5s)

sample148.0ms

Algorithm
intervals
Results
59.0ms270×body80valid
28.0ms36×body640valid
28.0ms24×body1280valid
12.0ms20×body320valid
3.0ms10×body160valid

simplify320.0ms

Calls
1 calls:
Slowest
319.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize41.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u insert-posit16 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
Calls
4 calls:
Slowest
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.2s

Calls
4 calls:
Slowest
578.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
501.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
124.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.4s

Calls
34 calls:
Slowest
496.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (* R R) R))
454.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
265.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
261.0ms
(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* phi1 (* R phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)) (/ (* phi1 (* lambda2 (* R phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))))))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
0.4b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Calls
4 calls:
Slowest
16.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
14.0ms
(cos (/ (+ phi2 phi1) 2))
9.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))

series109.0ms

Calls
4 calls:
Slowest
33.0ms
(cos (/ (+ phi2 phi1) 2))
28.0ms
(cos (/ (+ phi2 phi1) 2))
25.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Calls
15 calls:
Slowest
365.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
353.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
311.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
293.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
91.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
0.2b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
11×pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×sqrt-prod
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
Calls
4 calls:
Slowest
21.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
16.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
15.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))

series1.7s

Calls
4 calls:
Slowest
975.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
648.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
28.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify4.1s

Calls
37 calls:
Slowest
442.0ms
(* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))) (* (* R R) R))
332.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
329.0ms
(* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))) (* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)))
322.0ms
(- (+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* phi1 (* R phi2)) (* (cos (* 1/2 (+ phi1 phi2))) lambda1)) (/ (* phi1 (* lambda2 (* R phi2))) (* (cos (* 1/2 (+ phi1 phi2))) (pow lambda1 2))))))
321.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.6b

localize78.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
10.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(cos (/ (+ phi2 phi1) 2))

series118.0ms

Calls
4 calls:
Slowest
36.0ms
(cos (/ (+ phi2 phi1) 2))
32.0ms
(cos (/ (+ phi2 phi1) 2))
28.0ms
(cos (/ (+ phi2 phi1) 2))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Calls
12 calls:
Slowest
386.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
352.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
351.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
311.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
32.0ms
(cos (* 1/2 (+ phi1 phi2)))

prune1.1s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 2.6b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch5.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.9s8443×body80valid
1.4s1280×body640valid
1.2s784×body1280valid
547.0ms735×body320valid
142.0ms325×body160valid