Details

Time bar (total: 27.3s)

sample186.0ms

Algorithm
intervals
Results
72.0ms272×body80valid
46.0ms51×body640valid
21.0ms17×body1280valid
18.0ms28×body320valid
4.0ms9×body160valid

simplify722.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
722.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b
(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))

rewrite59.0ms

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
Counts
4 → 67
Calls
4 calls:
Slowest
36.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
10.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
623.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
543.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
141.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
45.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.4s

Counts
34 → 79
Calls
34 calls:
Slowest
431.0ms
(* (* (* (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))
392.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
366.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
338.0ms
(- (+ (* 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))))))
270.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize77.0ms

Local error

Found 4 expressions with local error:

2.4b
(cos (/ (+ phi2 phi1) 2))
2.4b
(cos (/ (+ phi2 phi1) 2))
2.4b
(cos (/ (+ phi2 phi1) 2))
0.4b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite72.0ms

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
23.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
17.0ms
(cos (/ (+ phi2 phi1) 2))
15.0ms
(cos (/ (+ phi2 phi1) 2))
15.0ms
(cos (/ (+ phi2 phi1) 2))

series156.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
42.0ms
(cos (/ (+ phi2 phi1) 2))
38.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
38.0ms
(cos (/ (+ phi2 phi1) 2))
38.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.8s

Counts
15 → 56
Calls
15 calls:
Slowest
404.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
390.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
301.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
70.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize43.0ms

Local error

Found 4 expressions with local error:

2.4b
(cos (/ (+ phi2 phi1) 2))
0.5b
(log (exp (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2)))))
0.1b
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2)) R)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
10×pow1 associate-*r*
9×log-prod
8×add-cbrt-cube associate-*l* add-exp-log log-pow
6×exp-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- rem-log-exp flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 84
Calls
4 calls:
Slowest
53.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2)))))
35.0ms
(log (exp (cos (/ (+ phi2 phi1) 2))))
12.0ms
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2)) R)
8.0ms
(cos (/ (+ phi2 phi1) 2))

series904.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
683.0ms
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2)) R)
143.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2)))))
41.0ms
(log (exp (cos (/ (+ phi2 phi1) 2))))
38.0ms
(cos (/ (+ phi2 phi1) 2))

simplify4.1s

Counts
51 → 96
Calls
51 calls:
Slowest
525.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2)) (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2))) (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2))))) (- phi1 phi2))) (* (* R R) R))
350.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log (exp (cos (/ (+ phi2 phi1) 2)))) (log (exp (cos (/ (+ phi2 phi1) 2))))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
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))))))
310.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log (exp (cos (/ (+ phi2 phi1) 2)))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

localize80.0ms

Local error

Found 4 expressions with local error:

2.4b
(cos (/ (+ phi2 phi1) 2))
2.4b
(cos (/ (+ phi2 phi1) 2))
2.4b
(cos (/ (+ phi2 phi1) 2))
2.4b
(cos (/ (+ phi2 phi1) 2))

rewrite39.0ms

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
Counts
4 → 40
Calls
4 calls:
Slowest
14.0ms
(cos (/ (+ phi2 phi1) 2))
9.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(cos (/ (+ phi2 phi1) 2))

series149.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
39.0ms
(cos (/ (+ phi2 phi1) 2))
38.0ms
(cos (/ (+ phi2 phi1) 2))
37.0ms
(cos (/ (+ phi2 phi1) 2))
36.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Counts
12 → 52
Calls
12 calls:
Slowest
424.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
357.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
333.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
326.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
37.0ms
(cos (* 1/2 (+ phi1 phi2)))

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.7b

regimes813.0ms

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 4.0b

bsearch6.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.6s8342×body80valid
1.7s781×body1280valid
1.4s1316×body640valid
525.0ms755×body320valid
159.0ms355×body160valid