Details

Time bar (total: 30.1s)

sample139.0ms

Algorithm
intervals
Results
47.0ms257×body80valid
36.0ms35×body640valid
16.0ms15×body1280valid
12.0ms21×body320valid
6.0ms16×body160valid

simplify399.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
399.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.0b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

rewrite57.0ms

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
39.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
9.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
8.0ms
(cos (/ (+ phi2 phi1) 2))

series813.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
652.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
136.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
25.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.2s

Counts
31 → 65
Calls
31 calls:
Slowest
509.0ms
(* (* (* (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))
400.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
387.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
351.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
277.0ms
(- (+ (* 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))))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize26.0ms

Local error

Found 3 expressions with local error:

2.5b
(cos (* (+ phi1 phi2) 1/2))
0.2b
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
0.0b
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)

rewrite62.0ms

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
46.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
10.0ms
(cos (* (+ phi1 phi2) 1/2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)

series833.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
681.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
129.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
22.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.5s

Counts
31 → 65
Calls
31 calls:
Slowest
487.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
422.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (* R R) R))
361.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
342.0ms
(- (+ (* 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))))))
302.0ms
(+ (* lambda2 (* (cos (* 1/2 (+ phi1 phi2))) R)) (+ (/ (* R (* phi1 phi2)) (* lambda1 (cos (* 1/2 (+ phi1 phi2))))) (/ (* R (* lambda2 (* phi1 phi2))) (* (pow lambda1 2) (cos (* 1/2 (+ phi1 phi2)))))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

localize66.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (* (+ phi1 phi2) 1/2))
2.5b
(cos (* (+ phi1 phi2) 1/2))
2.5b
(cos (* (+ phi1 phi2) 1/2))
0.5b
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))

rewrite139.0ms

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
Counts
4 → 44
Calls
4 calls:
Slowest
99.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
14.0ms
(cos (* (+ phi1 phi2) 1/2))
13.0ms
(cos (* (+ phi1 phi2) 1/2))
11.0ms
(cos (* (+ phi1 phi2) 1/2))

series136.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
43.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
37.0ms
(cos (* (+ phi1 phi2) 1/2))
33.0ms
(cos (* (+ phi1 phi2) 1/2))
24.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify2.3s

Counts
15 → 56
Calls
15 calls:
Slowest
444.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
436.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
434.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
380.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
294.0ms
(cbrt (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (cos (* (+ phi1 phi2) 1/2))))

prune1000.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (* (+ phi1 phi2) 1/2))
2.5b
(cos (* (+ phi1 phi2) 1/2))
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)

rewrite76.0ms

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 (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
21.0ms
(cos (* (+ phi1 phi2) 1/2))
15.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)
10.0ms
(cos (* (+ phi1 phi2) 1/2))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
916.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)
704.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
33.0ms
(cos (* (+ phi1 phi2) 1/2))
25.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.3s

Counts
37 → 81
Calls
37 calls:
Slowest
416.0ms
(* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (* (* R R) R))
400.0ms
(* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (* (* R R) R)))
368.0ms
(* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)))) (* (* (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)))
315.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
309.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.5b

regimes779.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.1s8421×body80valid
1.4s1286×body640valid
1.3s772×body1280valid
960.0ms754×body320valid
166.0ms369×body160valid