Details

Time bar (total: 3.3m)

sample166.0ms

Algorithm
intervals
Results
78.0ms88×body1280valid
29.0ms59×body640valid
29.0ms265×body80valid
12.0ms34×body320valid
4.0ms15×body160valid

simplify156.0ms

Calls
1 calls:
Slowest
156.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
160×add-sqr-sqrt
92×times-frac
76×*-un-lft-identity add-cube-cbrt
58×sqrt-prod
50×associate-*l*
38×unswap-sqr
36×associate-*r*
32×add-cbrt-cube add-exp-log
24×associate-/r* associate-*l/
14×pow1
12×swap-sqr prod-exp cbrt-unprod associate-/l*
10×*-commutative
6×cbrt-undiv div-exp pow-prod-down
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
4 calls:
Slowest
45.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
39.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
11.0ms
(/ (cos th) (sqrt 2))
10.0ms
(/ (cos th) (sqrt 2))

series480.0ms

Calls
4 calls:
Slowest
160.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
155.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
85.0ms
(/ (cos th) (sqrt 2))
80.0ms
(/ (cos th) (sqrt 2))

simplify11.7s

Calls
274 calls:
Slowest
728.0ms
(* (* (* (/ (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))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
609.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
563.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
385.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
632×sqrt-prod
622×times-frac
394×add-sqr-sqrt
352×*-un-lft-identity add-cube-cbrt
43×associate-/l*
39×associate-/r*
25×add-cbrt-cube associate-*l* add-exp-log
19×unswap-sqr
18×associate-*r*
15×associate-/l/
14×div-inv
12×associate-*l/
9×pow1
7×cbrt-undiv div-exp
6×swap-sqr prod-exp cbrt-unprod
5×clear-num frac-2neg *-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down
Calls
4 calls:
Slowest
36.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
22.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms
(/ (cos th) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt 2))

series469.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (cos th) (sqrt (sqrt 2)))
136.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
88.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
82.0ms
(/ (cos th) (sqrt 2))

simplify31.1s

Calls
824 calls:
Slowest
653.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
554.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) a2) (* (* a2 a2) a2)))
410.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
408.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
382.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))

prune8.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
809×sqrt-prod
796×times-frac
483×add-sqr-sqrt
441×*-un-lft-identity add-cube-cbrt
192×cbrt-prod
43×associate-/l*
42×associate-/r*
31×add-exp-log
25×add-cbrt-cube associate-*l*
19×unswap-sqr
18×associate-*r*
17×div-inv
15×associate-/l/
13×pow1
12×associate-*l/
11×div-exp
7×cbrt-undiv sqrt-pow1 pow-flip
6×swap-sqr prod-exp cbrt-unprod
5×clear-num frac-2neg *-commutative
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2 pow-prod-down
2×rec-exp pow1/3 1-exp pow-div
1×inv-pow
Calls
4 calls:
Slowest
41.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
9.0ms
(/ (cos th) (sqrt 2))
6.0ms
(/ 1 (sqrt (sqrt 2)))

series259.0ms

Calls
4 calls:
Slowest
148.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
110.0ms
(/ (cos th) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify40.9s

Calls
1019 calls:
Slowest
644.0ms
(* (* (* (/ (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)))
579.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (cbrt 1)))
354.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
353.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (cbrt (sqrt 2)))) (cbrt (sqrt (cbrt (sqrt 2))))))

prune12.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))) (sqrt (sqrt 2)))
0.7b
(/ (cos th) (sqrt (sqrt 2)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
1383×sqrt-prod
1326×times-frac
717×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
192×cbrt-prod
74×associate-/l*
57×associate-/r*
30×associate-/l/
27×div-inv
24×add-exp-log
18×add-cbrt-cube
12×div-exp
8×pow1 cbrt-undiv
7×sqrt-pow1 pow-flip
6×clear-num frac-2neg
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2
2×rec-exp pow1/3 1-exp pow-div
1×inv-pow
Calls
4 calls:
Slowest
26.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
16.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
14.0ms
(/ (cos th) (sqrt (sqrt 2)))
7.0ms
(/ 1 (sqrt (sqrt 2)))

series272.0ms

Calls
4 calls:
Slowest
160.0ms
(/ (cos th) (sqrt (sqrt 2)))
112.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.0m

Calls
1569 calls:
Slowest
488.0ms
(/ (/ 1 (sqrt (sqrt (* (cbrt 2) (cbrt 2))))) 1)
419.0ms
(/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
365.0ms
(- (+ (/ 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))))
319.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (cbrt (sqrt 2)))) (cbrt (sqrt (cbrt (sqrt 2))))))

prune18.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes367.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch10.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.9s2490×body1280valid
1.8s2104×body640valid
1.6s7951×body80valid
670.0ms1040×body320valid
158.0ms474×body160valid