Details

Time bar (total: 27.3s)

sample180.0ms

Algorithm
intervals
Results
56.0ms263×body80valid
50.0ms23×body1280valid
28.0ms29×body640valid
14.0ms22×body320valid
4.0ms10×body160valid

simplify295.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
295.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize54.0ms

Local error

Found 4 expressions with local error:

2.6b
(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))

rewrite34.0ms

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
19.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (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
665.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
537.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
125.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
35.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.6s

Counts
34 → 79
Calls
34 calls:
Slowest
493.0ms
(* (* (* (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))
421.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
371.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
300.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi2 phi1) 2)))
292.0ms
(+ (* 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)))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize44.0ms

Local error

Found 4 expressions with local error:

2.6b
(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))

rewrite86.0ms

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
59.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
20.0ms
(cos (* (+ phi1 phi2) 1/2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
639.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
528.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
142.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
32.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.2s

Counts
34 → 79
Calls
34 calls:
Slowest
567.0ms
(* (- (pow lambda1 3) (pow lambda2 3)) (cos (* (+ phi1 phi2) 1/2)))
476.0ms
(* (* (* (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))
445.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
348.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
313.0ms
(- (+ (* 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

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

localize61.0ms

Local error

Found 4 expressions with local error:

2.6b
(cos (/ (+ phi2 phi1) 2))
2.6b
(cos (/ (+ phi2 phi1) 2))
2.6b
(cos (/ (+ phi2 phi1) 2))
0.5b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))

rewrite66.0ms

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
Counts
4 → 44
Calls
4 calls:
Slowest
21.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
15.0ms
(cos (/ (+ phi2 phi1) 2))
15.0ms
(cos (/ (+ phi2 phi1) 2))
15.0ms
(cos (/ (+ phi2 phi1) 2))

series120.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
37.0ms
(cos (/ (+ phi2 phi1) 2))
33.0ms
(cos (/ (+ phi2 phi1) 2))
27.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Counts
15 → 56
Calls
15 calls:
Slowest
358.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
341.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
338.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
329.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))
69.0ms
(cbrt (* (+ (cos (+ (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2))) (cos (- (/ (+ phi2 phi1) 2) (/ (+ phi2 phi1) 2)))) (cos (/ (+ phi2 phi1) 2))))

prune976.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

localize94.0ms

Local error

Found 4 expressions with local error:

2.6b
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
2.6b
(cos (/ (+ phi1 phi2) 2))
2.6b
(cos (/ (+ phi1 phi2) 2))
1.0b
(cbrt 2)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×cos-sum pow1/3
Counts
4 → 45
Calls
4 calls:
Slowest
74.0ms
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
14.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
1.0ms
(cbrt 2)

series81.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
39.0ms
(cos (/ (+ phi1 phi2) 2))
23.0ms
(cos (/ (+ phi1 phi2) 2))
18.0ms
(cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2)))
0.0ms
(cbrt 2)

simplify1.2s

Counts
14 → 55
Calls
14 calls:
Slowest
346.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
315.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
215.0ms
(* (hypot (* (- lambda1 lambda2) (/ (cbrt (fma (cos (/ (+ phi1 phi2) 2)) (cos (+ (/ (+ phi1 phi2) 2) (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))) (cbrt 2))) (- phi1 phi2)) R)
208.0ms
(- 1 (+ (* phi1 phi2) (* 1/2 (pow phi1 2))))
31.0ms
(cos (* 1/2 (+ phi1 phi2)))

prune1.2s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 2.8b

regimes876.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.9s8330×body80valid
1.8s1323×body640valid
1.1s757×body1280valid
645.0ms731×body320valid
189.0ms358×body160valid