Details

Time bar (total: 24.9s)

sample240.0ms

Algorithm
intervals
Results
76.0ms296×body80valid
56.0ms50×body640valid
51.0ms21×body1280valid
18.0ms24×body320valid
6.0ms12×body160valid

simplify1.2s

Counts
1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize33.0ms

Local error

Found 4 expressions with local error:

2.5b
(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))

rewrite45.0ms

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
29.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
614.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
494.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
113.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
31.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.2s

Counts
79 → 79

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize29.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 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
30.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
11.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
7.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
758.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
541.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
133.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
37.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts
79 → 79

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize67.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
0.5b
(log1p (cos (/ (+ phi2 phi1) 2)))
0.2b
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))

rewrite24.0ms

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*
4×insert-posit16 log1p-expm1-u 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
15.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
8.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
73.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
59.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
27.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Counts
71 → 71

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

localize33.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi2 phi1) 2))
0.6b
(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
0.5b
(cbrt (- lambda1 lambda2))
0.5b
(cbrt (- lambda1 lambda2))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
34×add-sqr-sqrt
32×*-un-lft-identity
16×cbrt-div
14×add-cube-cbrt
11×pow1
10×swap-sqr
8×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
6×add-exp-log difference-of-squares
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 105
Calls
4 calls:
Slowest
39.0ms
(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
12.0ms
(cos (/ (+ phi2 phi1) 2))
3.0ms
(cbrt (- lambda1 lambda2))
3.0ms
(cbrt (- lambda1 lambda2))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(cbrt (- lambda1 lambda2))
177.0ms
(cbrt (- lambda1 lambda2))
146.0ms
(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
29.0ms
(cos (/ (+ phi2 phi1) 2))

simplify852.0ms

Counts
117 → 117

prune2.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.6b

regimes776.0ms

Accuracy

0% (0.1b remaining)

Error of 3.8b against oracle of 3.7b and baseline of 3.8b

bsearch11.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.3s8272×body80valid
1.5s747×body1280valid
1.4s1275×body640valid
944.0ms727×body320valid
206.0ms427×body160valid