Details

Time bar (total: 35.7s)

sample397.0ms

Algorithm
intervals
Results
137.0ms54×body1280valid
66.0ms55×body640valid
46.0ms162×body80valid
16.0ms19×body320valid
5.0ms9×body160valid

simplify132.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
131.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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)))

rewrite72.0ms

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
Counts
3 → 84
Calls
3 calls:
Slowest
46.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms
(/ x (tan B))
11.0ms
(/ 1 (sin B))

series300.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
143.0ms
(/ x (tan B))
139.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms
(/ 1 (sin B))

simplify2.3s

Counts
81 → 93
Calls
81 calls:
Slowest
375.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
328.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
123.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
85.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
84.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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/
Counts
4 → 174
Calls
4 calls:
Slowest
38.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
18.0ms
(/ 1 (/ (tan B) x))
11.0ms
(/ (tan B) x)
10.0ms
(/ 1 (sin B))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
122.0ms
(/ 1 (/ (tan B) x))
75.0ms
(/ (tan B) x)
14.0ms
(/ 1 (sin B))

simplify9.9s

Counts
207 → 186
Calls
207 calls:
Slowest
821.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
492.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))
481.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
385.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))
298.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
29×*-un-lft-identity times-frac
28×add-cube-cbrt
21×add-exp-log
14×associate-*l*
13×add-cbrt-cube
8×pow1
6×associate-/r* div-exp associate-/l* add-log-exp
4×prod-exp insert-posit16
3×cbrt-undiv rec-exp 1-exp associate-*r* div-inv unswap-sqr
2×clear-num frac-2neg associate-*l/ tan-quot associate-/r/ cbrt-unprod pow-flip inv-pow
1×sub-neg flip3-- diff-log pow-prod-down *-commutative frac-sub flip--
Counts
4 → 116
Calls
4 calls:
Slowest
25.0ms
(* (/ 1 (tan B)) x)
22.0ms
(- (/ 1 (sin B)) (* (/ 1 (tan B)) x))
6.0ms
(/ 1 (tan B))
5.0ms
(/ 1 (sin B))

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(- (/ 1 (sin B)) (* (/ 1 (tan B)) x))
119.0ms
(* (/ 1 (tan B)) x)
37.0ms
(/ 1 (tan B))
19.0ms
(/ 1 (sin B))

simplify3.6s

Counts
98 → 128
Calls
98 calls:
Slowest
440.0ms
(* (* (* (/ 1 (tan B)) (/ 1 (tan B))) (/ 1 (tan B))) (* (* x x) x))
359.0ms
(* (/ (* (* 1 1) 1) (* (* (tan B) (tan B)) (tan B))) (* (* x x) x))
351.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
284.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
242.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ 1 (tan B)) x)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube associate-*l*
7×pow1
6×associate-/r* associate-/l* add-log-exp
4×div-exp insert-posit16
3×cbrt-undiv associate-*r* associate-*l/ div-inv
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 108
Calls
4 calls:
Slowest
30.0ms
(* (/ x (sin B)) (cos B))
25.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (sin B))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
113.0ms
(* (/ x (sin B)) (cos B))
94.0ms
(/ x (sin B))
24.0ms
(/ 1 (sin B))

simplify3.1s

Counts
93 → 120
Calls
93 calls:
Slowest
448.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
374.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
263.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
205.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
200.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.2s1763×body1280valid
1.9s1475×body640valid
1.6s4870×body80valid
663.0ms703×body320valid
186.0ms350×body160valid