Details

Time bar (total: 5.5m)

sample247.0ms

Algorithm
intervals
Results
83.0ms76×body1280valid
73.0ms69×body640valid
44.0ms253×body80valid
18.0ms33×body320valid
7.0ms18×body160valid

simplify156.0ms

Calls
1 calls:
Slowest
156.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

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))
0.2b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
18×add-cbrt-cube add-exp-log
8×pow1
6×associate-/r* associate-/l*
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
5.0ms
(/ (cos th) (sqrt 2))
4.0ms
(/ (cos th) (sqrt 2))

series228.0ms

Calls
4 calls:
Slowest
74.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
71.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
46.0ms
(/ (cos th) (sqrt 2))
38.0ms
(/ (cos th) (sqrt 2))

simplify4.7s

Calls
98 calls:
Slowest
667.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
533.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
324.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
318.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
215.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×associate-*l*
6×pow1 associate-/r*
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×cbrt-div prod-exp cbrt-unprod div-inv
2×clear-num frac-2neg associate-*l/
1×cbrt-prod frac-times pow1/3 associate-*r* pow-prod-down associate-*r/ cos-mult *-commutative associate-/l/
Calls
4 calls:
Slowest
21.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
7.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
7.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
4.0ms
(/ (cos th) (sqrt 2))

series500.0ms

Calls
4 calls:
Slowest
358.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
72.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
39.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
30.0ms
(/ (cos th) (sqrt 2))

simplify3.6s

Calls
74 calls:
Slowest
505.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
380.0ms
(- (+ (* 1/24 (* (* (cbrt 1/2) (pow th 4)) (pow (/ 1 (sqrt 2)) 1/3))) (* (cbrt 1/2) (pow (/ 1 (sqrt 2)) 1/3))) (* 1/2 (* (* (cbrt 1/2) (pow th 2)) (pow (/ 1 (sqrt 2)) 1/3))))
254.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
232.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (cos th) (cos th)) (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
199.0ms
(/ (* (* (* (cos th) (cos th)) (* (cos th) (cos th))) (* (cos th) (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (* (cos th) (cos th)) (sqrt 2))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
158×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
26×associate-/l*
16×add-cbrt-cube add-exp-log
15×associate-/r*
10×div-inv
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div clear-num frac-2neg
2×associate-/l/
1×cbrt-prod frac-times pow1/3 associate-*l/ prod-exp associate-*r/ cos-mult cbrt-unprod
Calls
4 calls:
Slowest
21.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
14.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series536.0ms

Calls
4 calls:
Slowest
378.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
77.0ms
(/ (cos th) (sqrt (sqrt 2)))
43.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
38.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify13.6s

Calls
373 calls:
Slowest
359.0ms
(- (+ (* 1/24 (* (* (cbrt 1/2) (pow th 4)) (pow (/ 1 (sqrt 2)) 1/3))) (* (cbrt 1/2) (pow (/ 1 (sqrt 2)) 1/3))) (* 1/2 (* (* (cbrt 1/2) (pow th 2)) (pow (/ 1 (sqrt 2)) 1/3))))
338.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
323.0ms
(/ (* (* (* (cos th) (cos th)) (cos th)) (* (* (cos th) (cos th)) (cos th))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
278.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
274.0ms
(/ (* (* (/ (cos th) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune4.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (* (cos th) (cos th)) (sqrt 2))
0.6b
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
5439×times-frac
4629×sqrt-prod
2470×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
206×associate-/l*
103×div-inv
20×add-cbrt-cube add-exp-log
18×associate-/r*
9×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div clear-num frac-2neg
2×associate-/l/
1×cbrt-prod frac-times pow1/3 associate-*l/ prod-exp associate-*r/ cos-mult cbrt-unprod
Calls
4 calls:
Slowest
33.0ms
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))
16.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
7.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
4.0ms
(/ (cos th) (sqrt (sqrt 2)))

series603.0ms

Calls
4 calls:
Slowest
430.0ms
(cbrt (* (/ (* (cos th) (cos th)) (sqrt 2)) (/ (cos th) 2)))
62.0ms
(/ (cos th) (sqrt (sqrt 2)))
58.0ms
(/ (* (cos th) (cos th)) (sqrt 2))
53.0ms
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))

simplify4.4m

Calls
3930 calls:
Slowest
724.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2)))))) (sqrt (sqrt (sqrt (sqrt 2)))))
593.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (sqrt (sqrt (sqrt (sqrt 2)))))
497.0ms
(/ (/ (/ (sqrt (cos th)) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt (sqrt 2))))) 1)
461.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2)))))) (sqrt (sqrt 1)))
459.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))) (sqrt (sqrt (sqrt (sqrt 2)))))

prune26.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.8s2533×body1280valid
1.6s2043×body640valid
1.1s8038×body80valid
376.0ms1039×body320valid
116.0ms536×body160valid