Details

Time bar (total: 48.1s)

sample238.0ms

Algorithm
intervals
Results
101.0ms81×body1280valid
46.0ms251×body80valid
44.0ms58×body640valid
19.0ms35×body320valid
6.0ms17×body160valid

simplify187.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
187.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
32×add-cbrt-cube add-exp-log
14×pow1
12×associate-/r* prod-exp cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 172
Calls
4 calls:
Slowest
47.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
40.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
156.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
83.0ms
(/ (cos th) (sqrt 2))
74.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 184
Calls
180 calls:
Slowest
669.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
641.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
628.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
611.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
328.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) a2)
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
74×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
25×add-cbrt-cube add-exp-log
12×associate-/r*
11×pow1
8×prod-exp cbrt-unprod
6×associate-/l* unswap-sqr
5×cbrt-undiv div-exp
4×associate-*r* pow-prod-down insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 169
Calls
4 calls:
Slowest
35.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
16.0ms
(* (/ (cos th) (sqrt 2)) a2)
11.0ms
(/ (cos th) (sqrt 2))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
150.0ms
(* (/ (cos th) (sqrt 2)) a2)
86.0ms
(/ (cos th) (sqrt 2))
71.0ms
(/ (cos th) (sqrt 2))

simplify6.8s

Counts
177 → 181
Calls
177 calls:
Slowest
630.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
584.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
314.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
314.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
305.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt 2))
0.4b
(* (/ (cos th) (sqrt 2)) a1)
0.3b
(* (/ (cos th) (sqrt 2)) a2)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
76×times-frac
62×*-un-lft-identity add-cube-cbrt
44×associate-*l* sqrt-prod
18×add-cbrt-cube add-exp-log
12×associate-/r*
8×pow1
6×associate-*r* associate-/l* unswap-sqr
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative
Counts
4 → 166
Calls
4 calls:
Slowest
17.0ms
(/ (cos th) (sqrt 2))
16.0ms
(* (/ (cos th) (sqrt 2)) a2)
16.0ms
(* (/ (cos th) (sqrt 2)) a1)
13.0ms
(/ (cos th) (sqrt 2))

series806.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
501.0ms
(* (/ (cos th) (sqrt 2)) a2)
139.0ms
(* (/ (cos th) (sqrt 2)) a1)
100.0ms
(/ (cos th) (sqrt 2))
65.0ms
(/ (cos th) (sqrt 2))

simplify4.9s

Counts
174 → 178
Calls
174 calls:
Slowest
301.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
282.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
272.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
252.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a2 a2) a2))
241.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (* 2 (sqrt 2)))
0.4b
(* (cbrt (* (* (cos th) (cos th)) (/ (cos th) (* 2 (sqrt 2))))) a1)
0.3b
(* (/ (cos th) (sqrt 2)) a2)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
41×times-frac
37×*-un-lft-identity add-cube-cbrt
26×associate-*l*
22×sqrt-prod
18×add-exp-log
17×add-cbrt-cube
8×pow1
7×associate-/r*
6×associate-*r* associate-/l*
5×associate-*l/
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×cbrt-div div-inv
2×clear-num frac-2neg pow-prod-down cos-mult *-commutative
1×cbrt-prod frac-times associate-*r/
Counts
4 → 128
Calls
4 calls:
Slowest
34.0ms
(* (cbrt (* (* (cos th) (cos th)) (/ (cos th) (* 2 (sqrt 2))))) a1)
25.0ms
(* (/ (cos th) (sqrt 2)) a2)
17.0ms
(/ (cos th) (sqrt 2))
11.0ms
(/ (cos th) (* 2 (sqrt 2)))

series862.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
552.0ms
(* (cbrt (* (* (cos th) (cos th)) (/ (cos th) (* 2 (sqrt 2))))) a1)
140.0ms
(* (/ (cos th) (sqrt 2)) a2)
99.0ms
(/ (cos th) (* 2 (sqrt 2)))
71.0ms
(/ (cos th) (sqrt 2))

simplify6.6s

Counts
119 → 140
Calls
119 calls:
Slowest
551.0ms
(* (* (* (cos th) (cos th)) (/ (cos th) (* 2 (sqrt 2)))) (* (* a1 a1) a1))
532.0ms
(* (* (cbrt 1/2) (* a1 (cos th))) (pow (/ 1 (sqrt 2)) 1/3))
466.0ms
(* (* (cbrt 1/2) (* a1 (cos th))) (pow (/ 1 (sqrt 2)) 1/3))
359.0ms
(* (cbrt (* (+ (cos (+ th th)) (cos (- th th))) (/ (cos th) (* 2 (sqrt 2))))) a1)
299.0ms
(- (+ (* 1/2 (/ 1 (sqrt 2))) (* 1/48 (/ (pow th 4) (sqrt 2)))) (* 1/4 (/ (pow th 2) (sqrt 2))))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes701.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.4s2579×body1280valid
1.9s2148×body640valid
1.8s8172×body80valid
565.0ms1030×body320valid
198.0ms494×body160valid