Details

Time bar (total: 41.1s)

sample238.0ms

Algorithm
intervals
Results
68.0ms250×body80valid
49.0ms42×body640valid
42.0ms27×body1280valid
36.0ms27×body320valid
10.0ms19×body160valid

simplify410.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
410.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize49.0ms

Local error

Found 3 expressions with local error:

2.0b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×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×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 56
Calls
3 calls:
Slowest
44.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
17.0ms
(cos (/ (+ phi2 phi1) 2))
13.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

series811.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
664.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
117.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
31.0ms
(cos (/ (+ phi2 phi1) 2))

simplify7.7s

Counts
65 → 65
Calls
65 calls:
Slowest
1.0s
(* (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))) (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
706.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
441.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
426.0ms
(* (* (* (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))
399.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R) (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)) (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize67.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi2 phi1) 2))
2.0b
(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)

rewrite69.0ms

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
Counts
4 → 69
Calls
4 calls:
Slowest
29.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
16.0ms
(cos (/ (+ phi2 phi1) 2))
16.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
941.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
627.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
27.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify8.6s

Counts
81 → 81
Calls
81 calls:
Slowest
627.0ms
(* (* (* (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))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)))
521.0ms
(* (* (* (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))
382.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
363.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
359.0ms
(* (* (* (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)))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.8b

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi2 phi1) 2))
0.6b
(cbrt (- lambda1 lambda2))
0.6b
(cbrt (- lambda1 lambda2))
0.6b
(cbrt (- lambda1 lambda2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 64
Calls
4 calls:
Slowest
14.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(cbrt (- lambda1 lambda2))
6.0ms
(cbrt (- lambda1 lambda2))
6.0ms
(cbrt (- lambda1 lambda2))

series734.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
241.0ms
(cbrt (- lambda1 lambda2))
225.0ms
(cbrt (- lambda1 lambda2))
220.0ms
(cbrt (- lambda1 lambda2))
48.0ms
(cos (/ (+ phi2 phi1) 2))

simplify4.6s

Counts
94 → 76
Calls
94 calls:
Slowest
488.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))
451.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))
444.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
404.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))
402.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.8b

localize88.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (/ (+ phi2 phi1) 2))
2.0b
(cos (/ (+ phi2 phi1) 2))
2.0b
(cos (/ (+ phi2 phi1) 2))
0.6b
(cbrt (- lambda1 lambda2))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×cbrt-prod add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div
1×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 48
Calls
4 calls:
Slowest
9.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))
3.0ms
(cbrt (- lambda1 lambda2))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(cbrt (- lambda1 lambda2))
26.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.1s

Counts
66 → 60
Calls
66 calls:
Slowest
432.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
418.0ms
(- (exp (* 1/3 (+ (log -1) (log lambda2)))) (+ (* 1/9 (* (exp (* 1/3 (- (log -1) (* 5 (log lambda2))))) (pow lambda1 2))) (* 1/3 (* (exp (* 1/3 (- (log -1) (* 2 (log lambda2))))) lambda1))))
418.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
406.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
293.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 2.8b

regimes947.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch4.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.5s8340×body80valid
1.5s1271×body640valid
1.5s782×body1280valid
618.0ms724×body320valid
142.0ms318×body160valid