Details

Time bar (total: 29.3s)

sample140.0ms

Algorithm
intervals
Results
48.0ms54×body640valid
36.0ms247×body80valid
22.0ms26×body1280valid
9.0ms19×body320valid
5.0ms18×body160valid

simplify301.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
301.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b
(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))

rewrite53.0ms

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
25.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
17.0ms
(cos (/ (+ phi2 phi1) 2))
10.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
633.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
478.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
133.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.6s

Counts
34 → 79
Calls
34 calls:
Slowest
545.0ms
(* (* (* (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))
434.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
365.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
334.0ms
(- (+ (* 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)) (cos (/ (+ phi2 phi1) 2)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize40.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
0.4b
(log1p (cos (/ (+ phi2 phi1) 2)))
0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
0.2b
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u associate-*l*
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
Slowest
16.0ms
(cos (/ (+ phi2 phi1) 2))
15.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
82.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
65.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
34.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Counts
27 → 71
Calls
27 calls:
Slowest
350.0ms
(- (log 2) (+ (* 1/8 (* phi1 phi2)) (* 1/16 (pow phi2 2))))
315.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
312.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))) (expm1 (log1p (cos (/ (+ phi2 phi1) 2))))) (expm1 (log1p (cos (/ (+ phi2 phi1) 2))))))
291.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
226.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize71.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (* (+ phi1 phi2) 1/2))
0.4b
(log1p (cos (* (+ phi1 phi2) 1/2)))
0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2)))))
0.2b
(expm1 (log1p (cos (* (+ phi1 phi2) 1/2))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u associate-*l*
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
Slowest
23.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2)))))
19.0ms
(cos (* (+ phi1 phi2) 1/2))
1.0ms
(log1p (cos (* (+ phi1 phi2) 1/2)))
0.0ms
(expm1 (log1p (cos (* (+ phi1 phi2) 1/2))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2)))))
80.0ms
(log1p (cos (* (+ phi1 phi2) 1/2)))
72.0ms
(expm1 (log1p (cos (* (+ phi1 phi2) 1/2))))
22.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify2.5s

Counts
27 → 71
Calls
27 calls:
Slowest
407.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (expm1 (log1p (cos (* (+ phi1 phi2) 1/2)))) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2))))) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2))))))
385.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
365.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
304.0ms
(- (log 2) (+ (* 1/8 (* phi1 phi2)) (* 1/16 (pow phi1 2))))
268.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (expm1 (log1p (cos (* (+ phi1 phi2) 1/2)))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize45.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
2.5b
(cos (/ (+ phi2 phi1) 2))
0.4b
(* (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)

rewrite80.0ms

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
37.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
14.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
14.0ms
(cos (/ (+ phi2 phi1) 2))
14.0ms
(cos (/ (+ phi2 phi1) 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
915.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
654.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
42.0ms
(cos (/ (+ phi2 phi1) 2))
34.0ms
(cos (/ (+ phi2 phi1) 2))

simplify4.0s

Counts
37 → 81
Calls
37 calls:
Slowest
395.0ms
(* (* (* (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))
387.0ms
(* (* (* (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)))
311.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
305.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
296.0ms
(- (+ (* 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))))))

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.7b

regimes770.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch3.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.7s8297×body80valid
1.8s1298×body640valid
1.1s765×body1280valid
556.0ms726×body320valid
211.0ms375×body160valid