Details

Time bar (total: 42.6s)

sample214.0ms

Algorithm
intervals
Results
88.0ms261×body80valid
40.0ms39×body640valid
37.0ms26×body1280valid
16.0ms21×body320valid
3.0ms8×body160valid

simplify310.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
310.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi2 phi1) 2))
0.1b
(* (- 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
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
7.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
633.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
559.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
97.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
39.0ms
(cos (/ (+ phi2 phi1) 2))

simplify8.5s

Counts
79 → 79
Calls
79 calls:
Slowest
941.0ms
(* (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))) (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))))
528.0ms
(* (* (* (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))
425.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
374.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R) (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)) (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R))
370.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi2 2))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (* (+ phi1 phi2) 1/2))
0.1b
(* (- 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))

rewrite50.0ms

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
33.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
9.0ms
(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
616.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
565.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
122.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
33.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify8.8s

Counts
79 → 79
Calls
79 calls:
Slowest
878.0ms
(* (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (- lambda1 lambda2)) (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
379.0ms
(* (* (* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R) (* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)) (* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R))
368.0ms
(+ (* (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))) (* (- phi1 phi2) (- phi1 phi2)))
320.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
300.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (* (+ phi1 phi2) 1/2)))

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.2b

localize35.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (* (+ phi1 phi2) 1/2))
0.5b
(expm1 (cos (* (+ phi1 phi2) 1/2)))
0.2b
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
0.1b
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))

rewrite45.0ms

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×associate-*l* log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
Slowest
25.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
17.0ms
(cos (* (+ phi1 phi2) 1/2))
1.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
0.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
60.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
56.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
23.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify4.8s

Counts
69 → 71
Calls
69 calls:
Slowest
380.0ms
(* (* (* (- 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))))))
342.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
324.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
301.0ms
(exp (* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))))
245.0ms
(* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.2b

localize71.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (* (+ phi1 phi2) 1/2))
3.0b
(cos (* (+ phi1 phi2) 1/2))
3.0b
(cos (* (+ phi1 phi2) 1/2))
0.4b
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))

rewrite157.0ms

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
98.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
20.0ms
(cos (* (+ phi1 phi2) 1/2))
19.0ms
(cos (* (+ phi1 phi2) 1/2))
19.0ms
(cos (* (+ phi1 phi2) 1/2))

series157.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
41.0ms
(cos (* (+ phi1 phi2) 1/2))
40.0ms
(cos (* (+ phi1 phi2) 1/2))
38.0ms
(cbrt (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (cos (* (+ phi1 phi2) 1/2))))
37.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.9s

Counts
56 → 56
Calls
56 calls:
Slowest
359.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
353.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
345.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
332.0ms
(- 1 (+ (* 1/4 (* phi1 phi2)) (* 1/8 (pow phi1 2))))
329.0ms
(cbrt (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (cos (* (+ phi1 phi2) 1/2))))

prune929.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.2b

regimes878.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.3s8365×body80valid
2.1s806×body1280valid
1.5s1312×body640valid
487.0ms729×body320valid
148.0ms345×body160valid