Details

Time bar (total: 23.7s)

sample198.0ms

Algorithm
intervals
Results
60.0ms278×body80valid
40.0ms45×body640valid
39.0ms21×body320valid
32.0ms25×body1280valid
5.0ms12×body160valid

simplify265.0ms

Calls
1 calls:
Slowest
265.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b
(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))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/ *-commutative
1×hypot-udef flip3-- pow-prod-down prod-exp cbrt-unprod flip--
Calls
4 calls:
Slowest
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
5.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
4.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series960.0ms

Calls
4 calls:
Slowest
497.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
353.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
81.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
30.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Calls
24 calls:
Slowest
338.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
312.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
255.0ms
(- (+ (* 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))))))
232.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
231.0ms
(+ (* 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)))))))

prune982.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize25.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.3b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- expm1-udef
Calls
4 calls:
Slowest
5.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
2.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series243.0ms

Calls
4 calls:
Slowest
126.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
51.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
47.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
19.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.8s

Calls
24 calls:
Slowest
285.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))) (log1p (expm1 (cos (/ (+ phi2 phi1) 2))))))
259.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
258.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
243.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
225.0ms
(- E (+ (* 1/8 (* E (pow phi2 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(cos (/ (+ phi2 phi1) 2))
0.5b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite23.0ms

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
Calls
4 calls:
Slowest
9.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
4.0ms
(cos (/ (+ phi2 phi1) 2))
4.0ms
(cos (/ (+ phi2 phi1) 2))
4.0ms
(cos (/ (+ phi2 phi1) 2))

series92.0ms

Calls
4 calls:
Slowest
26.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
24.0ms
(cos (/ (+ phi2 phi1) 2))
24.0ms
(cos (/ (+ phi2 phi1) 2))
18.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Calls
15 calls:
Slowest
406.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
360.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
316.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
74.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune995.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

localize12.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi2 phi1) 2))
3.5b
(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)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l*
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×associate-*r* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
4.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
2.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(cos (/ (+ phi2 phi1) 2))

series1.3s

Calls
4 calls:
Slowest
751.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
498.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
23.0ms
(cos (/ (+ phi2 phi1) 2))
20.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.9s

Calls
25 calls:
Slowest
450.0ms
(cos (* 1/2 (+ phi1 phi2)))
368.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
365.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
298.0ms
(- (+ (* 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))))))
292.0ms
(* (* (* (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)))

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.3b

regimes901.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.6s8398×body80valid
1.8s1361×body640valid
1.3s825×body1280valid
571.0ms755×body320valid
142.0ms362×body160valid