Details

Time bar (total: 34.6s)

sample190.0ms

Algorithm
intervals
Results
62.0ms279×body80valid
57.0ms27×body640valid
23.0ms33×body320valid
21.0ms16×body1280valid
6.0ms13×body160valid

simplify276.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
276.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize54.0ms

Local error

Found 4 expressions with local error:

4.2b
(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))

rewrite41.0ms

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
20.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
12.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
660.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
518.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
155.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
37.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.5s

Counts
34 → 79
Calls
34 calls:
Slowest
531.0ms
(* (* (* (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))
476.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
356.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
293.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
268.0ms
(- (+ (* 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

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize29.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (* (+ phi1 phi2) 1/2))
0.2b
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
0.0b
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))

rewrite79.0ms

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
55.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
10.0ms
(cos (* (+ phi1 phi2) 1/2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
723.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
572.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
130.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
37.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.7s

Counts
34 → 79
Calls
34 calls:
Slowest
483.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
415.0ms
(* (* (* (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))
371.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
309.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (* (+ phi1 phi2) 1/2)))
293.0ms
(- (+ (* 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))))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize48.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (* (+ phi1 phi2) 1/2))
0.5b
(cbrt (- lambda1 lambda2))
0.5b
(cbrt (- lambda1 lambda2))
0.5b
(cbrt (- lambda1 lambda2))

rewrite37.0ms

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
20.0ms
(cos (* (+ phi1 phi2) 1/2))
6.0ms
(cbrt (- lambda1 lambda2))
6.0ms
(cbrt (- lambda1 lambda2))
4.0ms
(cbrt (- lambda1 lambda2))

series668.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
223.0ms
(cbrt (- lambda1 lambda2))
222.0ms
(cbrt (- lambda1 lambda2))
198.0ms
(cbrt (- lambda1 lambda2))
24.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.2s

Counts
33 → 76
Calls
33 calls:
Slowest
645.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
581.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 lambda1)))))
564.0ms
(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))))
396.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

localize60.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (* (+ phi1 phi2) 1/2))
4.2b
(cos (* (+ phi1 phi2) 1/2))
0.4b
(* (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)

rewrite101.0ms

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
45.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
20.0ms
(cos (* (+ phi1 phi2) 1/2))
20.0ms
(cos (* (+ phi1 phi2) 1/2))
15.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
854.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)
37.0ms
(cos (* (+ phi1 phi2) 1/2))
37.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.1s

Counts
37 → 81
Calls
37 calls:
Slowest
378.0ms
(* (* (* (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)))
373.0ms
(* (* (* (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))
341.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
315.0ms
(* (* (* (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)))
292.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

regimes887.0ms

Accuracy

0% (0.2b remaining)

Error of 4.1b against oracle of 3.9b and baseline of 4.1b

bsearch4.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.6s8399×body80valid
1.5s1300×body640valid
1.1s796×body1280valid
666.0ms753×body320valid
585.0ms346×body160valid