Details

Time bar (total: 6.2m)

sample175.0ms

Algorithm
intervals
Results
74.0ms76×body1280valid
37.0ms69×body640valid
31.0ms253×body80valid
12.0ms33×body320valid
4.0ms18×body160valid

simplify135.0ms

Calls
1 calls:
Slowest
134.0ms
(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-*l*
18×add-cbrt-cube add-exp-log
8×pow1
6×associate-/r* associate-/l*
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r* pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
13.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms
(/ (cos th) (sqrt 2))
7.0ms
(/ (cos th) (sqrt 2))

series232.0ms

Calls
4 calls:
Slowest
74.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
74.0ms
(* (/ (cos th) (sqrt 2)) (* a2 a2))
49.0ms
(/ (cos th) (sqrt 2))
36.0ms
(/ (cos th) (sqrt 2))

simplify4.4s

Calls
98 calls:
Slowest
583.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
557.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a2 a2) (* a2 a2)) (* a2 a2)))
263.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
242.0ms
(* (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
203.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos th) (sqrt 2))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.3b
(* (/ (cos th) (sqrt 2)) (* a1 a1))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
294×times-frac
171×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
28×associate-/l*
18×add-cbrt-cube add-exp-log
15×associate-/r*
13×associate-*l*
11×div-inv
6×pow1 cbrt-undiv div-exp
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×prod-exp cbrt-unprod
1×associate-*r* pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
14.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
13.0ms
(/ (cos th) (sqrt 2))
8.0ms
(/ (cos th) (sqrt (sqrt 2)))

series248.0ms

Calls
4 calls:
Slowest
81.0ms
(* (/ (cos th) (sqrt 2)) (* a1 a1))
79.0ms
(/ (cos th) (sqrt (sqrt 2)))
52.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
36.0ms
(/ (cos th) (sqrt 2))

simplify13.8s

Calls
397 calls:
Slowest
572.0ms
(* (* (* (/ (cos th) (sqrt 2)) (/ (cos th) (sqrt 2))) (/ (cos th) (sqrt 2))) (* (* (* a1 a1) (* a1 a1)) (* a1 a1)))
301.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
284.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
223.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))
220.0ms
(- (+ (/ 1 (sqrt 2)) (* 1/24 (/ (pow th 4) (sqrt 2)))) (* 1/2 (/ (pow th 2) (sqrt 2))))

prune4.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
552×times-frac
308×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
288×sqrt-prod
50×associate-/l*
24×associate-/r*
18×add-cbrt-cube add-exp-log div-inv
8×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
8.0ms
(/ (cos th) (sqrt (sqrt 2)))
5.0ms
(/ (cos th) (sqrt (sqrt 2)))

series213.0ms

Calls
4 calls:
Slowest
77.0ms
(/ (cos th) (sqrt (sqrt 2)))
57.0ms
(/ (cos th) (sqrt (sqrt 2)))
43.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
35.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify22.8s

Calls
696 calls:
Slowest
404.0ms
(/ (* (cbrt (/ (cos th) (sqrt (sqrt 2)))) (cbrt (/ (cos th) (sqrt (sqrt 2))))) 1)
310.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
300.0ms
(/ (/ (* (* (cos th) (cos th)) (cos th)) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
295.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))
276.0ms
(- (+ (sqrt (/ 1 (sqrt 2))) (* 1/24 (* (sqrt (/ 1 (sqrt 2))) (pow th 4)))) (* 1/2 (* (sqrt (/ 1 (sqrt 2))) (pow th 2))))

prune6.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))
0.6b
(/ (cos th) (sqrt (sqrt 2)))
0.6b
(/ (cos th) (sqrt (sqrt 2)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
5712×times-frac
4773×sqrt-prod
2620×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
230×associate-/l*
111×div-inv
27×associate-/r*
22×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
Calls
4 calls:
Slowest
36.0ms
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))
22.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms
(/ (cos th) (sqrt (sqrt 2)))
8.0ms
(/ (cos th) (sqrt (sqrt 2)))

series222.0ms

Calls
4 calls:
Slowest
68.0ms
(/ (cos th) (sqrt (sqrt 2)))
62.0ms
(/ (cos th) (sqrt (sqrt 2)))
52.0ms
(/ (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))) (sqrt (sqrt (sqrt 2))))
39.0ms
(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify4.7m

Calls
4253 calls:
Slowest
739.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (sqrt (sqrt (sqrt (sqrt 2)))))
714.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (sqrt (sqrt (sqrt 2)))) (sqrt (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2)))))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2))))))
484.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2)))))) (sqrt (sqrt 1)))
471.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (sqrt (sqrt (sqrt 2)))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2)))))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2))))))
470.0ms
(/ (/ (/ (* (cbrt (cos th)) (cbrt (cos th))) (* (cbrt (sqrt (sqrt 2))) (cbrt (sqrt (sqrt 2))))) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (sqrt 2))))))

prune27.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.0s2533×body1280valid
1.3s2043×body640valid
1.0s8038×body80valid
477.0ms1039×body320valid
151.0ms536×body160valid