Details

Time bar (total: 23.7s)

sample187.0ms

Algorithm
intervals
Results
55.0ms263×body80valid
52.0ms40×body640valid
33.0ms26×body1280valid
15.0ms21×body320valid
4.0ms11×body160valid

simplify1.0s

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize49.0ms

Local error

Found 3 expressions with local error:

2.3b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

rewrite42.0ms

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
Counts
3 → 56
Calls
3 calls:
Slowest
22.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
12.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)

series797.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
641.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
123.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
33.0ms
(cos (/ (+ phi2 phi1) 2))

simplify917.0ms

Counts
65 → 65

prune885.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize41.0ms

Local error

Found 3 expressions with local error:

2.3b
(cos (* 1/2 (+ phi1 phi2)))
0.2b
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)

rewrite66.0ms

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×cos-sum pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 58
Calls
3 calls:
Slowest
45.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
8.0ms
(cos (* 1/2 (+ phi1 phi2)))

series785.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
642.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
105.0ms
(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
38.0ms
(cos (* 1/2 (+ phi1 phi2)))

simplify1.0s

Counts
67 → 67

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.1b
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.1b
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
0.1b
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity
11×associate-*l*
10×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
9×flip3-- associate-*r* cos-mult flip-- sin-mult
8×frac-times
6×add-log-exp
4×expm1-log1p-u associate-*r/ frac-sub insert-posit16 log1p-expm1-u sub-div
3×distribute-rgt-in sub-neg distribute-lft-in prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*l/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
Slowest
322.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
58.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
49.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
23.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
409.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
143.0ms
(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
81.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
77.0ms
(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))

simplify888.0ms

Counts
118 → 118

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.2b
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.2b
(expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))
0.1b
(* (- lambda1 lambda2) (expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))

rewrite42.0ms

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*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef expm1-log1p flip3-- log1p-expm1 flip-- sin-mult distribute-lft-out-- expm1-udef difference-of-squares
Counts
4 → 71
Calls
4 calls:
Slowest
25.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
15.0ms
(* (- lambda1 lambda2) (expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))
1.0ms
(log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.0ms
(expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))

series836.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
421.0ms
(* (- lambda1 lambda2) (expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))
167.0ms
(expm1 (log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))
167.0ms
(log1p (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
81.0ms
(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify1.6s

Counts
83 → 83

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes800.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch8.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.2s1260×body640valid
2.1s8318×body80valid
1.3s839×body1280valid
1000.0ms741×body320valid
258.0ms374×body160valid