Details

Time bar (total: 22.4s)

sample187.0ms

Algorithm
intervals
Results
79.0ms267×body80valid
31.0ms39×body640valid
29.0ms28×body1280valid
18.0ms30×body320valid
6.0ms16×body160valid

simplify271.0ms

Calls
1 calls:
Slowest
271.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b
(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))

rewrite18.0ms

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
8.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
2.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series891.0ms

Calls
4 calls:
Slowest
435.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
356.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
82.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
18.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.5s

Calls
24 calls:
Slowest
377.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
337.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
284.0ms
(* (- (* 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))))))
268.0ms
(+ (* 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

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
0.3b
(log1p (cos (/ (+ phi2 phi1) 2)))
0.2b
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u 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
10.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
4.0ms
(cos (/ (+ phi2 phi1) 2))
1.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))

series296.0ms

Calls
4 calls:
Slowest
141.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
64.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
61.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
30.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.3s

Calls
24 calls:
Slowest
382.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
368.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))) (expm1 (log1p (cos (/ (+ phi2 phi1) 2))))) (expm1 (log1p (cos (/ (+ phi2 phi1) 2))))))
353.0ms
(- (log 2) (+ (* 1/8 (* phi1 phi2)) (* 1/16 (pow phi2 2))))
322.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
312.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
0.4b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite16.0ms

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))))
2.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(cos (/ (+ phi2 phi1) 2))

series95.0ms

Calls
4 calls:
Slowest
24.0ms
(cos (/ (+ phi2 phi1) 2))
24.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
24.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Calls
15 calls:
Slowest
356.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
335.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
294.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
58.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
3.0b
(cos (/ (+ phi2 phi1) 2))
0.5b
(cbrt (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))))

rewrite18.0ms

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 cos-mult
Calls
4 calls:
Slowest
6.0ms
(cbrt (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))))
5.0ms
(cos (/ (+ phi2 phi1) 2))
4.0ms
(cos (/ (+ phi2 phi1) 2))
3.0ms
(cos (/ (+ phi2 phi1) 2))

series199.0ms

Calls
4 calls:
Slowest
128.0ms
(cbrt (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))))
25.0ms
(cos (/ (+ phi2 phi1) 2))
24.0ms
(cos (/ (+ phi2 phi1) 2))
22.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Calls
14 calls:
Slowest
368.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
344.0ms
(- 1 (+ (* 1/6 (* phi1 phi2)) (* 1/12 (pow phi2 2))))
338.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
284.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
48.0ms
(pow (pow (cos (* 1/2 (+ phi1 phi2))) 2) 1/3)

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.5b

regimes931.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.2s8406×body80valid
1.9s1261×body640valid
1.2s774×body1280valid
1.0s752×body320valid
168.0ms410×body160valid