Details

Time bar (total: 3.0m)

sample232.0ms

Algorithm
intervals
Results
88.0ms75×body1280valid
53.0ms72×body640valid
44.0ms259×body80valid
20.0ms34×body320valid
5.0ms14×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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
32.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
25.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
17.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series486.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
131.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
99.0ms
(/ (cos th) (sqrt 2))
83.0ms
(/ (cos th) (sqrt 2))

simplify8.5s

Counts
180 → 184
Calls
180 calls:
Slowest
666.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
614.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
614.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
591.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
355.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.2b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
616×sqrt-prod
614×times-frac
345×add-sqr-sqrt
340×*-un-lft-identity add-cube-cbrt
37×associate-/l*
25×add-cbrt-cube add-exp-log
24×associate-/r*
22×associate-*l*
14×div-inv
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 473
Calls
4 calls:
Slowest
43.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
34.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt 2))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
139.0ms
(/ (cos th) (sqrt (sqrt 2)))
89.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
76.0ms
(/ (cos th) (sqrt 2))

simplify27.9s

Counts
765 → 485
Calls
765 calls:
Slowest
650.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
588.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
512.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
449.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (sqrt (sqrt (sqrt 2)))) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
365.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune7.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
1.0b
(/ 1 (sqrt (sqrt 2)))
0.7b
(/ (cos th) (sqrt 2))
0.2b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
793×sqrt-prod
788×times-frac
434×add-sqr-sqrt
429×*-un-lft-identity add-cube-cbrt
192×cbrt-prod
37×associate-/l*
31×add-exp-log
27×associate-/r*
25×add-cbrt-cube
22×associate-*l*
17×div-inv
13×pow1
11×div-exp
7×cbrt-undiv sqrt-pow1 pow-flip
6×prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow1/2 pow-prod-down unswap-sqr
2×rec-exp pow1/3 1-exp pow-div
1×associate-*r* associate-*l/ *-commutative inv-pow associate-/l/
Counts
4 → 581
Calls
4 calls:
Slowest
32.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms
(/ (cos th) (sqrt 2))
12.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
6.0ms
(/ 1 (sqrt (sqrt 2)))

series223.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
142.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
81.0ms
(/ (cos th) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify37.3s

Counts
960 → 589
Calls
960 calls:
Slowest
685.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
681.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
521.0ms
(+ (- (log (cos th)) (log (sqrt 2))) (+ (log a2) (log a2)))
392.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
364.0ms
(/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (cbrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt 2)))))

prune10.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
1.0b
(/ 1 (sqrt (sqrt 2)))
0.7b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
1365×sqrt-prod
1326×times-frac
709×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
192×cbrt-prod
68×associate-/l*
39×associate-/r*
27×div-inv
24×add-exp-log
18×add-cbrt-cube
12×div-exp
8×pow1 cbrt-undiv
7×sqrt-pow1 pow-flip
4×clear-num frac-2neg insert-posit16 add-log-exp
3×pow1/2
2×rec-exp pow1/3 1-exp pow-div associate-/l/
1×inv-pow
Counts
4 → 882
Calls
4 calls:
Slowest
29.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
18.0ms
(/ (cos th) (sqrt (sqrt 2)))
12.0ms
(/ 1 (sqrt (sqrt 2)))

series243.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
176.0ms
(/ (cos th) (sqrt (sqrt 2)))
67.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify55.2s

Counts
1545 → 890
Calls
1545 calls:
Slowest
557.0ms
(/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))
433.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
418.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (cbrt (sqrt 2)))) (cbrt (sqrt (cbrt (sqrt 2))))))
391.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
308.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune17.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes533.0ms

Accuracy

0% (0.4b remaining)

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

bsearch9.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.2s2508×body1280valid
2.6s2055×body640valid
1.7s8001×body80valid
620.0ms1084×body320valid
184.0ms532×body160valid