Details

Time bar (total: 24.6s)

sample1.0s

Algorithm
intervals
Results
460.0ms14×body160valid
228.0ms60×body1280valid
74.0ms47×body640valid
58.0ms151×body80valid
27.0ms23×body320valid

simplify175.0ms

Calls
1 calls:
Slowest
174.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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
20×prod-diff
18×*-un-lft-identity
17×add-sqr-sqrt
15×add-cube-cbrt
13×div-inv
6×associate-/r*
5×tan-quot associate-/r/ add-log-exp
4×pow1 fma-neg add-exp-log
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×clear-num frac-2neg distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log frac-sub pow-flip flip-- inv-pow difference-of-squares
Calls
3 calls:
Slowest
26.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
4.0ms
(/ x (tan B))
2.0ms
(/ 1 (sin B))

series300.0ms

Calls
3 calls:
Slowest
147.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
137.0ms
(/ x (tan B))
15.0ms
(/ 1 (sin B))

simplify3.7s

Calls
66 calls:
Slowest
119.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (cos B) (/ x (sin B)))))
118.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))
110.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
103.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (tan B)) 1)))
102.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))

prune888.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1 add-exp-log
6×associate-/r* add-cbrt-cube add-log-exp
5×div-inv
4×expm1-log1p-u fma-neg associate-*l* prod-diff insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l/
2×clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod pow-flip flip-- inv-pow sub-div
Calls
4 calls:
Slowest
18.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
5.0ms
(* (/ x (sin B)) (cos B))
1.0ms
(/ 1 (sin B))
0.0ms
(/ x (sin B))

series309.0ms

Calls
4 calls:
Slowest
117.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
111.0ms
(* (/ x (sin B)) (cos B))
67.0ms
(/ x (sin B))
14.0ms
(/ 1 (sin B))

simplify1.7s

Calls
43 calls:
Slowest
199.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
169.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
138.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
101.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
93.0ms
(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

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)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1 add-exp-log
6×associate-/r* add-cbrt-cube add-log-exp
5×div-inv
4×expm1-log1p-u fma-neg associate-*l* prod-diff insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l/
2×clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod pow-flip flip-- inv-pow sub-div
Calls
4 calls:
Slowest
11.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
5.0ms
(* (/ x (sin B)) (cos B))
1.0ms
(/ 1 (sin B))
0.0ms
(/ x (sin B))

series365.0ms

Calls
4 calls:
Slowest
139.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
131.0ms
(* (/ x (sin B)) (cos B))
71.0ms
(/ x (sin B))
24.0ms
(/ 1 (sin B))

simplify1.9s

Calls
43 calls:
Slowest
226.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
223.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
120.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))
119.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
111.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (/ 1 (tan B)))
0.2b
(/ 1 (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* x (/ 1 (tan B))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 associate-/r* add-exp-log add-log-exp
5×associate-*r* div-inv
4×expm1-log1p-u add-cbrt-cube fma-neg prod-diff insert-posit16 log1p-expm1-u
2×rec-exp clear-num frac-2neg tan-quot associate-*r/ associate-/r/ un-div-inv frac-sub pow-flip inv-pow
1×sub-neg flip3-- diff-log *-commutative flip--
Calls
4 calls:
Slowest
16.0ms
(- (/ 1 (sin B)) (* x (/ 1 (tan B))))
3.0ms
(* x (/ 1 (tan B)))
2.0ms
(/ 1 (tan B))
2.0ms
(/ 1 (sin B))

series363.0ms

Calls
4 calls:
Slowest
150.0ms
(- (/ 1 (sin B)) (* x (/ 1 (tan B))))
142.0ms
(* x (/ 1 (tan B)))
42.0ms
(/ 1 (tan B))
29.0ms
(/ 1 (sin B))

simplify1.8s

Calls
43 calls:
Slowest
344.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
114.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
110.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
108.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
107.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))

prune920.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes113.0ms

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
3.6s1692×body1280valid
2.0s1450×body640valid
1.9s4912×body80valid
691.0ms718×body320valid
240.0ms358×body160valid