Details

Time bar (total: 3.4m)

sample238.0ms

Algorithm
intervals
Results
64.0ms78×body640valid
63.0ms74×body1280valid
33.0ms222×body80valid
18.0ms38×body320valid
4.0ms13×body160valid

simplify561.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
561.0ms
(+ (* (/ (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

localize47.0ms

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

rewrite113.0ms

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
42.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
26.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
25.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series477.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
135.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
93.0ms
(/ (cos th) (sqrt 2))
80.0ms
(/ (cos th) (sqrt 2))

simplify8.6s

Counts
180 → 192
Calls
180 calls:
Slowest
682.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
643.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
577.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
414.0ms
(- (+ (/ 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

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) (* a2 a2))

rewrite90.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down unswap-sqr
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 481
Calls
4 calls:
Slowest
23.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
21.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt 2))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(/ (cos th) (sqrt (sqrt 2)))
130.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
109.0ms
(/ (cos th) (sqrt 2))
78.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify28.7s

Counts
765 → 493
Calls
765 calls:
Slowest
690.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
656.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
480.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
402.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
386.0ms
(- (+ (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

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
1143×sqrt-prod
1125×times-frac
615×add-sqr-sqrt
581×*-un-lft-identity add-cube-cbrt
283×associate-*l*
37×add-cbrt-cube add-exp-log
35×associate-/l*
24×associate-/r*
23×div-inv
13×unswap-sqr
12×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
9×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
Slowest
35.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
26.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
17.0ms
(/ (cos th) (sqrt (sqrt 2)))
12.0ms
(/ (* a2 (cos th)) (sqrt 2))

series927.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
485.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
170.0ms
(/ (cos th) (sqrt (sqrt 2)))
156.0ms
(/ (* a2 (cos th)) (sqrt 2))
116.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))

simplify45.9s

Counts
1026 → 756
Calls
1026 calls:
Slowest
456.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
410.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
405.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a1) (log a1)))
398.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
383.0ms
(+ (- (log (/ (cos th) (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a1) (log a1)))

prune11.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
1.0b
(/ 1 (sqrt (sqrt 2)))
0.5b
(/ (* a2 (cos th)) (sqrt 2))
0.3b
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a1 a1))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
1525×sqrt-prod
1504×times-frac
827×add-sqr-sqrt
770×*-un-lft-identity
758×add-cube-cbrt
392×cbrt-prod
376×associate-*l*
57×add-exp-log
37×add-cbrt-cube
35×associate-/l*
29×div-inv unswap-sqr
27×associate-/r*
22×div-exp
16×prod-exp
13×pow1
12×cbrt-undiv
10×cbrt-unprod
7×sqrt-pow1 pow-flip
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow1/2 pow-prod-down
2×pow1/3 pow-div
1×associate-*r* associate-*l/ *-commutative inv-pow associate-/l/
Counts
4 → 965
Calls
4 calls:
Slowest
53.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a1 a1))
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
17.0ms
(/ (* a2 (cos th)) (sqrt 2))
12.0ms
(/ 1 (sqrt (sqrt 2)))

series1.0s

Counts
4 → 8
Calls
4 calls:
Slowest
873.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a1 a1))
153.0ms
(/ (* a2 (cos th)) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.1m

Counts
1350 → 973
Calls
1350 calls:
Slowest
547.0ms
(+ (- (- 0 (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (+ (log a1) (log a1)))
511.0ms
(+ (- (- 0 (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (log (* a1 a1)))
492.0ms
(+ (- (- (log 1) (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (log (* a1 a1)))
478.0ms
(+ (- (- (log 1) (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (+ (log a1) (log a1)))
441.0ms
(/ (/ (sqrt 1) (sqrt (sqrt (sqrt 2)))) (sqrt 1))

prune18.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes515.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.4s2595×body1280valid
2.3s2163×body640valid
1.9s7804×body80valid
727.0ms1041×body320valid
213.0ms531×body160valid