Details

Time bar (total: 49.1s)

sample255.0ms

Algorithm
intervals
Results
117.0ms81×body1280valid
46.0ms58×body640valid
45.0ms251×body80valid
20.0ms35×body320valid
7.0ms17×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
140.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* associate-*l/ *-commutative
Counts
4 → 180
Calls
4 calls:
Slowest
47.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
39.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
19.0ms
(/ (cos th) (sqrt 2))
18.0ms
(/ (cos th) (sqrt 2))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
145.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms
(/ (cos th) (sqrt 2))
75.0ms
(/ (cos th) (sqrt 2))

simplify8.7s

Counts
180 → 192
Calls
180 calls:
Slowest
754.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
708.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
658.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
654.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
341.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite102.0ms

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×expm1-log1p-u associate-*r* pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 177
Calls
4 calls:
Slowest
52.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
26.0ms
(* (/ (cos th) (sqrt 2)) a2)
10.0ms
(/ (cos th) (sqrt 2))
10.0ms
(/ (cos th) (sqrt 2))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
142.0ms
(* (/ (cos th) (sqrt 2)) a2)
83.0ms
(/ (cos th) (sqrt 2))
78.0ms
(/ (cos th) (sqrt 2))

simplify7.3s

Counts
177 → 189
Calls
177 calls:
Slowest
711.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
666.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
395.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
384.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
282.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a2 a2) a2))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.5b
(/ (sqrt 2) a1)
0.3b
(* (/ (cos th) (sqrt 2)) a2)
0.2b
(* (* (/ (cos th) (sqrt 2)) a2) a2)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
56×times-frac
49×*-un-lft-identity add-cube-cbrt
34×sqrt-prod
23×associate-*l*
22×add-cbrt-cube add-exp-log
11×pow1
9×associate-/r* associate-/l*
7×prod-exp cbrt-unprod
6×associate-*r*
4×expm1-log1p-u cbrt-undiv div-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ div-inv unswap-sqr
2×clear-num frac-2neg *-commutative
Counts
4 → 153
Calls
4 calls:
Slowest
30.0ms
(* (* (/ (cos th) (sqrt 2)) a2) a2)
18.0ms
(/ (cos th) (sqrt 2))
14.0ms
(* (/ (cos th) (sqrt 2)) a2)
5.0ms
(/ (sqrt 2) a1)

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(* (* (/ (cos th) (sqrt 2)) a2) a2)
126.0ms
(* (/ (cos th) (sqrt 2)) a2)
78.0ms
(/ (cos th) (sqrt 2))
51.0ms
(/ (sqrt 2) a1)

simplify5.0s

Counts
150 → 165
Calls
150 calls:
Slowest
369.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
328.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a2 a2) a2))
312.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
270.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1))
266.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 2) a1)
0.3b
(/ (* (* (cos th) a2) a2) (sqrt 2))
0.2b
(/ (* (cos th) a1) (/ (sqrt 2) a1))
0.1b
(* (cos th) a1)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
82×times-frac
53×add-sqr-sqrt
51×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
31×associate-/r*
29×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
8×associate-/l*
6×pow1 prod-exp cbrt-unprod
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l*
1×pow-prod-down associate-/r/ *-commutative unswap-sqr
Counts
4 → 162
Calls
4 calls:
Slowest
45.0ms
(/ (* (* (cos th) a2) a2) (sqrt 2))
23.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
10.0ms
(/ (sqrt 2) a1)
9.0ms
(* (cos th) a1)

series728.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
457.0ms
(/ (* (cos th) a1) (/ (sqrt 2) a1))
143.0ms
(/ (* (* (cos th) a2) a2) (sqrt 2))
66.0ms
(/ (sqrt 2) a1)
62.0ms
(* (cos th) a1)

simplify6.9s

Counts
166 → 174
Calls
166 calls:
Slowest
354.0ms
(* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1))
336.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* a1 a1) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))
323.0ms
(/ (* (* (* (* (cos th) (cos th)) (cos th)) (* (* a2 a2) a2)) (* (* a2 a2) a2)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
311.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (* (* (/ (sqrt 2) a1) (/ (sqrt 2) a1)) (/ (sqrt 2) a1)))
304.0ms
(/ (* (* (* (cos th) a1) (* (cos th) a1)) (* (cos th) a1)) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a1 a1) a1)))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes478.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.3s2579×body1280valid
2.2s8172×body80valid
1.7s2148×body640valid
583.0ms1030×body320valid
173.0ms494×body160valid