Details

Time bar (total: 1.2m)

sample189.0ms

Algorithm
intervals
Results
59.0ms65×body1280valid
58.0ms57×body640valid
37.0ms262×body80valid
15.0ms35×body320valid
5.0ms17×body160valid

simplify140.0ms

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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

rewrite107.0ms

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
45.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
41.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series508.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
148.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
100.0ms
(/ (cos th) (sqrt 2))
98.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 192
Calls
180 calls:
Slowest
609.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
592.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
584.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
583.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
367.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

11 alts after pruning (11 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)) a1)
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite92.0ms

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
46.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
25.0ms
(* (/ (cos th) (sqrt 2)) a1)
11.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt 2))

series410.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
129.0ms
(* (/ (cos th) (sqrt 2)) a1)
86.0ms
(/ (cos th) (sqrt 2))
58.0ms
(/ (cos th) (sqrt 2))

simplify6.5s

Counts
177 → 189
Calls
177 calls:
Slowest
568.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
523.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
362.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
329.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
262.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a1 a1) a1))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
50×times-frac
41×*-un-lft-identity add-cube-cbrt
31×sqrt-prod
25×add-cbrt-cube associate-*l* add-exp-log
13×associate-*r*
12×associate-/r*
8×pow1
7×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp unswap-sqr
2×clear-num frac-2neg pow-prod-down *-commutative
1×associate-*l/ associate-*r/
Counts
4 → 150
Calls
4 calls:
Slowest
30.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
15.0ms
(* (/ (cos th) (sqrt 2)) a1)
15.0ms
(/ (* a2 (cos th)) (sqrt 2))
9.0ms
(/ (cos th) (sqrt 2))

series508.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(/ (* a2 (cos th)) (sqrt 2))
142.0ms
(* (/ (cos th) (sqrt 2)) a1)
140.0ms
(* a2 (/ (* a2 (cos th)) (sqrt 2)))
74.0ms
(/ (cos th) (sqrt 2))

simplify5.1s

Counts
137 → 162
Calls
137 calls:
Slowest
353.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
336.0ms
(* (* (* a2 a2) a2) (/ (* (* (* a2 (cos th)) (* a2 (cos th))) (* a2 (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))))
273.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
259.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* a1 a1) a1))
221.0ms
(- (/ a1 (sqrt 2)) (* 1/2 (/ (* a1 (pow th 2)) (sqrt 2))))

prune2.0s

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 (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) a1)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
349×add-sqr-sqrt
341×*-un-lft-identity add-cube-cbrt
37×associate-/l*
24×associate-/r*
22×associate-*l*
18×add-cbrt-cube add-exp-log
14×div-inv
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×prod-exp cbrt-unprod
1×pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 478
Calls
4 calls:
Slowest
24.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))
12.0ms
(* (/ (cos th) (sqrt 2)) a1)
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ (cos th) (sqrt (sqrt 2)))
132.0ms
(* (/ (cos th) (sqrt 2)) a1)
71.0ms
(/ (cos th) (sqrt 2))
67.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify27.9s

Counts
762 → 490
Calls
762 calls:
Slowest
572.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (sqrt (sqrt (sqrt 2)))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))
506.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
393.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
384.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
369.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))

prune7.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes643.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.1s2470×body1280valid
2.0s2140×body640valid
1.9s7994×body80valid
729.0ms1084×body320valid
187.0ms540×body160valid