Details

Time bar (total: 3.4m)

sample255.0ms

Algorithm
intervals
Results
86.0ms78×body640valid
84.0ms74×body1280valid
37.0ms222×body80valid
20.0ms38×body320valid
4.0ms13×body160valid

simplify127.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
127.0ms
(+ (* (/ (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

localize46.0ms

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))

rewrite104.0ms

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
34.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
24.0ms
(/ (cos th) (sqrt 2))
23.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
18.0ms
(/ (cos th) (sqrt 2))

series492.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
158.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
89.0ms
(/ (cos th) (sqrt 2))
84.0ms
(/ (cos th) (sqrt 2))

simplify9.0s

Counts
180 → 184
Calls
180 calls:
Slowest
919.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
664.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
657.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
629.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
318.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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
28.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
19.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt 2))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
121.0ms
(/ (cos th) (sqrt (sqrt 2)))
109.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
96.0ms
(/ (cos th) (sqrt 2))

simplify28.4s

Counts
765 → 485
Calls
765 calls:
Slowest
687.0ms
(* (* (* (/ (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))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
445.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
356.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
348.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune7.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

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))

rewrite171.0ms

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×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 736
Calls
4 calls:
Slowest
75.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
28.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
22.0ms
(/ (* a2 (cos th)) (sqrt 2))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
147.0ms
(/ (* a2 (cos th)) (sqrt 2))
122.0ms
(/ (cos th) (sqrt (sqrt 2)))
78.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify46.2s

Counts
1026 → 748
Calls
1026 calls:
Slowest
502.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
447.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (log (* a1 a1)))
418.0ms
(+ (- (- (log (cos th)) (log (sqrt (sqrt 2)))) (log (sqrt (sqrt 2)))) (+ (log a1) (log a1)))
358.0ms
(/ (cbrt (cos th)) (sqrt (cbrt (sqrt 2))))
356.0ms
(* (/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))

prune12.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

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))

rewrite153.0ms

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×rec-exp 1-exp insert-posit16 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 → 957
Calls
4 calls:
Slowest
48.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a1 a1))
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
21.0ms
(/ 1 (sqrt (sqrt 2)))
16.0ms
(/ (* a2 (cos th)) (sqrt 2))

series679.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
510.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a1 a1))
168.0ms
(/ (* 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 → 965
Calls
1350 calls:
Slowest
740.0ms
(/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (cbrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt 2)))))
575.0ms
(+ (- (- 0 (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (log (* a1 a1)))
560.0ms
(+ (- (- (log 1) (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (+ (log a1) (log a1)))
537.0ms
(+ (- (- 0 (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (+ (log a1) (log a1)))
503.0ms
(+ (- (- (log 1) (log (sqrt (sqrt 2)))) (log (sqrt (cbrt (sqrt 2))))) (log (* a1 a1)))

prune19.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes591.0ms

Accuracy

0% (0.4b remaining)

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

bsearch8.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.4s2595×body1280valid
2.5s2163×body640valid
1.5s7804×body80valid
560.0ms1041×body320valid
180.0ms531×body160valid