Details

Time bar (total: 54.4s)

sample305.0ms

Algorithm
intervals
Results
106.0ms72×body640valid
85.0ms69×body1280valid
53.0ms265×body80valid
20.0ms30×body320valid
18.0ms24×body160valid

simplify154.0ms

Calls
1 calls:
Slowest
154.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
11.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2))
4.0ms
(/ (cos th) (sqrt 2))

series472.0ms

Calls
4 calls:
Slowest
151.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
142.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
98.0ms
(/ (cos th) (sqrt 2))
82.0ms
(/ (cos th) (sqrt 2))

simplify4.6s

Calls
98 calls:
Slowest
552.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
530.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
260.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
222.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
216.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize8.0ms

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
13×add-cbrt-cube add-exp-log
6×pow1 associate-/r* associate-/l*
4×insert-posit16 div-inv add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg associate-*l/ prod-exp *-commutative cbrt-unprod
1×associate-*r* pow-prod-down
Calls
4 calls:
Slowest
13.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
10.0ms
(* (/ (cos th) (sqrt 2)) a2)
4.0ms
(/ (cos th) (sqrt 2))
4.0ms
(/ (cos th) (sqrt 2))

series499.0ms

Calls
4 calls:
Slowest
184.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
138.0ms
(* (/ (cos th) (sqrt 2)) a2)
95.0ms
(/ (cos th) (sqrt 2))
81.0ms
(/ (cos th) (sqrt 2))

simplify3.4s

Calls
93 calls:
Slowest
553.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
293.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
250.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
224.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
201.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.4b
(/ (* (cos th) a2) (sqrt 2))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b
(* (/ (* (cos th) a2) (sqrt 2)) a2)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×associate-*l*
13×add-cbrt-cube add-exp-log
6×pow1 associate-/r*
4×insert-posit16 div-inv associate-/l* add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg associate-*l/ prod-exp *-commutative cbrt-unprod
1×associate-*r* pow-prod-down
Calls
4 calls:
Slowest
16.0ms
(* (/ (* (cos th) a2) (sqrt 2)) a2)
16.0ms
(/ (* (cos th) a2) (sqrt 2))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
8.0ms
(/ (cos th) (sqrt 2))

series554.0ms

Calls
4 calls:
Slowest
171.0ms
(* (/ (* (cos th) a2) (sqrt 2)) a2)
162.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
117.0ms
(/ (* (cos th) a2) (sqrt 2))
103.0ms
(/ (cos th) (sqrt 2))

simplify3.3s

Calls
74 calls:
Slowest
623.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
251.0ms
(- (/ a2 (sqrt 2)) (* 1/2 (/ (* a2 (pow th 2)) (sqrt 2))))
233.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
209.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
172.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.4b
(/ (* (cos th) a2) (sqrt 2))
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
519×times-frac
281×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
264×sqrt-prod
136×associate-*l*
26×associate-/l*
22×add-cbrt-cube add-exp-log
17×div-inv
15×associate-/r*
8×cbrt-undiv div-exp
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg prod-exp cbrt-unprod
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
24.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
8.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
6.0ms
(/ (* (cos th) a2) (sqrt 2))
4.0ms
(/ (cos th) (sqrt (sqrt 2)))

series461.0ms

Calls
4 calls:
Slowest
142.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
134.0ms
(/ (* (cos th) a2) (sqrt 2))
108.0ms
(/ (cos th) (sqrt (sqrt 2)))
77.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify21.7s

Calls
509 calls:
Slowest
419.0ms
(+ (- (log (/ (cos th) (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
385.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
350.0ms
(/ (/ (* (* (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
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
299.0ms
(* (/ (* (* (/ (cos th) (sqrt (sqrt 2))) (/ (cos th) (sqrt (sqrt 2)))) (/ (cos th) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune5.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes422.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.3s2507×body1280valid
1.7s2065×body640valid
1.6s8082×body80valid
1.1s1066×body320valid
249.0ms540×body160valid