Details

Time bar (total: 3.1m)

sample198.0ms

Algorithm
intervals
Results
81.0ms75×body1280valid
44.0ms72×body640valid
33.0ms259×body80valid
15.0ms34×body320valid
4.0ms14×body160valid

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(+ (* (/ (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

localize43.0ms

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))

rewrite99.0ms

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
31.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
29.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms
(/ (cos th) (sqrt 2))
17.0ms
(/ (cos th) (sqrt 2))

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
179.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
107.0ms
(/ (cos th) (sqrt 2))
80.0ms
(/ (cos th) (sqrt 2))

simplify8.8s

Counts
180 → 192
Calls
180 calls:
Slowest
775.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
734.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
610.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) a1) (* (* a1 a1) a1)))
601.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
445.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize43.0ms

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))

rewrite91.0ms

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
31.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
15.0ms
(/ (cos th) (sqrt (sqrt 2)))
14.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
8.0ms
(/ (cos th) (sqrt 2))

series460.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
125.0ms
(/ (cos th) (sqrt (sqrt 2)))
106.0ms
(/ (cos th) (sqrt 2))
72.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify29.7s

Counts
765 → 493
Calls
765 calls:
Slowest
665.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
606.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
540.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
439.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
417.0ms
(/ (/ (cbrt (cos th)) (sqrt (sqrt 2))) (sqrt (sqrt (cbrt 2))))

prune7.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize93.0ms

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))

rewrite132.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 589
Calls
4 calls:
Slowest
43.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
26.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
17.0ms
(/ (cos th) (sqrt 2))
12.0ms
(/ 1 (sqrt (sqrt 2)))

series242.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
165.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
76.0ms
(/ (cos th) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify39.0s

Counts
960 → 597
Calls
960 calls:
Slowest
663.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
647.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
442.0ms
(/ (/ 1 (sqrt (sqrt (sqrt 2)))) (sqrt (cbrt (sqrt (sqrt 2)))))
435.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
416.0ms
(/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (cbrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt 2)))))

prune11.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize89.0ms

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)))

rewrite109.0ms

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×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2
2×rec-exp pow1/3 1-exp pow-div associate-/l/
1×inv-pow
Counts
4 → 890
Calls
4 calls:
Slowest
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
22.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
20.0ms
(/ 1 (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))

series218.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
139.0ms
(/ (cos th) (sqrt (sqrt 2)))
78.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify59.9s

Counts
1545 → 898
Calls
1545 calls:
Slowest
525.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
479.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
447.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
446.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt 2) (cbrt 2)))))
375.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (cbrt (sqrt 2)))) (cbrt (sqrt (cbrt (sqrt 2))))))

prune17.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes451.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.3s2508×body1280valid
2.2s2055×body640valid
2.0s8001×body80valid
727.0ms1084×body320valid
216.0ms532×body160valid