Details

Time bar (total: 31.2s)

sample292.0ms

Algorithm
intervals
Results
118.0ms60×body1280valid
85.0ms47×body640valid
44.0ms151×body80valid
20.0ms23×body320valid
10.0ms14×body160valid

simplify123.0ms

Calls
1 calls:
Slowest
122.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ x (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
27×times-frac
19×add-cube-cbrt
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×div-exp insert-posit16 div-inv distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp tan-quot associate-/r/ frac-sub pow-flip flip-- inv-pow
Calls
3 calls:
Slowest
23.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series303.0ms

Calls
3 calls:
Slowest
149.0ms
(/ x (tan B))
133.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
21.0ms
(/ 1 (sin B))

simplify2.1s

Calls
81 calls:
Slowest
393.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
331.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
111.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
84.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
73.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.1b
(/ (tan B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
111×add-sqr-sqrt
85×*-un-lft-identity
64×add-cube-cbrt
21×add-exp-log
19×associate-/r*
15×difference-of-squares
13×add-cbrt-cube
11×div-inv
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×insert-posit16
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot associate-/r/ frac-sub flip-- associate-/l/
Calls
4 calls:
Slowest
24.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
8.0ms
(/ (tan B) x)
6.0ms
(/ 1 (/ (tan B) x))
5.0ms
(/ 1 (sin B))

series372.0ms

Calls
4 calls:
Slowest
171.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
116.0ms
(/ 1 (/ (tan B) x))
63.0ms
(/ (tan B) x)
22.0ms
(/ 1 (sin B))

simplify8.5s

Calls
207 calls:
Slowest
460.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))
410.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))
348.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
337.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))
332.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.5b
(* (cbrt (tan B)) (cbrt (tan B)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
7×cbrt-div tan-quot
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
29.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
4.0ms
(cbrt (tan B))
4.0ms
(cbrt (tan B))
3.0ms
(cbrt (tan B))

series648.0ms

Calls
4 calls:
Slowest
190.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
155.0ms
(cbrt (tan B))
152.0ms
(cbrt (tan B))
151.0ms
(cbrt (tan B))

simplify2.1s

Calls
72 calls:
Slowest
333.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
277.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
239.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
213.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
196.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (tan B)))
0.6b
(cbrt (cbrt (tan B)))
0.6b
(cbrt (cbrt (tan B)))
0.6b
(cbrt (tan B))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×cbrt-div
4×pow1 add-cbrt-cube pow1/3 tan-quot add-exp-log insert-posit16 add-log-exp
Calls
4 calls:
Slowest
7.0ms
(cbrt (cbrt (tan B)))
4.0ms
(cbrt (cbrt (tan B)))
2.0ms
(cbrt (cbrt (tan B)))
2.0ms
(cbrt (tan B))

series921.0ms

Calls
4 calls:
Slowest
444.0ms
(cbrt (cbrt (tan B)))
179.0ms
(cbrt (cbrt (tan B)))
157.0ms
(cbrt (tan B))
141.0ms
(cbrt (cbrt (tan B)))

simplify1.5s

Calls
37 calls:
Slowest
245.0ms
(+ (* 1/27 (pow (pow B 19) 1/9)) (+ (* 34/3645 (pow (pow B 37) 1/9)) (pow B 1/9)))
239.0ms
(+ (* 1/27 (pow (pow B 19) 1/9)) (+ (* 34/3645 (pow (pow B 37) 1/9)) (pow B 1/9)))
216.0ms
(+ (* 1/27 (pow (pow B 19) 1/9)) (+ (* 34/3645 (pow (pow B 37) 1/9)) (pow B 1/9)))
193.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
64.0ms
(pow (/ (sin B) (cos B)) 1/3)

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch6.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.3s1692×body1280valid
1.8s1450×body640valid
1.4s4912×body80valid
1.3s718×body320valid
667.0ms358×body160valid