Details

Time bar (total: 27.9s)

sample196.0ms

Algorithm
intervals
Results
58.0ms257×body80valid
48.0ms33×body1280valid
34.0ms33×body640valid
21.0ms15×body160valid
10.0ms16×body320valid

simplify358.0ms

Calls
1 calls:
Slowest
358.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize38.0ms

Local error

Found 3 expressions with local error:

3.8b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×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×flip3-- flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
61.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
35.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

series811.0ms

Calls
3 calls:
Slowest
658.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
131.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
23.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.1s

Calls
31 calls:
Slowest
485.0ms
(* (* (* (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))
445.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
288.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
275.0ms
(- (+ (* 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))))))
273.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))

prune953.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize38.0ms

Local error

Found 3 expressions with local error:

3.8b
(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)

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×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×flip3-- flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
63.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
47.0ms
(cos (* (+ phi1 phi2) 1/2))
10.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)

series839.0ms

Calls
3 calls:
Slowest
672.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
145.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
22.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.5s

Calls
31 calls:
Slowest
529.0ms
(* (* (* (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))
492.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
397.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
312.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (* (+ phi1 phi2) 1/2)))
279.0ms
(- (+ (* 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))))))

prune893.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b
(cos (* (+ phi1 phi2) 1/2))
0.5b
(expm1 (cos (* (+ phi1 phi2) 1/2)))
0.3b
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))

rewrite77.0ms

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* log1p-expm1-u
4×insert-posit16 add-log-exp
3×associate-*r*
2×associate-*l/ log1p-expm1
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
52.0ms
(cos (* (+ phi1 phi2) 1/2))
23.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
1.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
1.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))

series386.0ms

Calls
4 calls:
Slowest
209.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
80.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
60.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
36.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify2.5s

Calls
28 calls:
Slowest
366.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))))
350.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
320.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
284.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
257.0ms
(- E (+ (* 1/8 (* E (pow phi1 2))) (+ (* 1/4 (* E (* phi1 phi2))) 1)))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

localize30.0ms

Local error

Found 4 expressions with local error:

3.8b
(cos (* (+ phi1 phi2) 1/2))
3.8b
(cos (* (+ phi1 phi2) 1/2))
3.8b
(cos (* (+ phi1 phi2) 1/2))
0.7b
(* (expm1 (cos (* (+ phi1 phi2) 1/2))) (expm1 (cos (* (+ phi1 phi2) 1/2))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l*
1×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
40.0ms
(cos (* (+ phi1 phi2) 1/2))
24.0ms
(cos (* (+ phi1 phi2) 1/2))
23.0ms
(cos (* (+ phi1 phi2) 1/2))
8.0ms
(* (expm1 (cos (* (+ phi1 phi2) 1/2))) (expm1 (cos (* (+ phi1 phi2) 1/2))))

series241.0ms

Calls
4 calls:
Slowest
139.0ms
(* (expm1 (cos (* (+ phi1 phi2) 1/2))) (expm1 (cos (* (+ phi1 phi2) 1/2))))
42.0ms
(cos (* (+ phi1 phi2) 1/2))
39.0ms
(cos (* (+ phi1 phi2) 1/2))
22.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.3s

Calls
33 calls:
Slowest
617.0ms
(pow (- (exp (cos (* 1/2 (+ phi1 phi2)))) 1) 2)
361.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
347.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
332.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
306.0ms
(- (+ (pow E 2) (+ (* 1/2 (* E (* phi1 phi2))) (+ (* 1/4 (* E (pow phi1 2))) 1))) (+ (* 1/2 (* (pow E 2) (* phi1 phi2))) (+ (* 1/4 (* (pow E 2) (pow phi1 2))) (* 2 E))))

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.2b

regimes896.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch4.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.1s8250×body80valid
1.5s1312×body640valid
1.4s702×body320valid
1.4s808×body1280valid
190.0ms378×body160valid