Details

Time bar (total: 2.3m)

sample464.0ms

Algorithm
intervals
Results
133.0ms50×body640valid
130.0ms63×body1280valid
49.0ms158×body80valid
22.0ms18×body320valid
5.0ms8×body160valid

simplify162.0ms

Calls
1 calls:
Slowest
161.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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
15.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
3.0ms
(/ x (tan B))
2.0ms
(/ 1 (sin B))

series363.0ms

Calls
3 calls:
Slowest
191.0ms
(/ x (tan B))
147.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms
(/ 1 (sin B))

simplify4.5s

Calls
66 calls:
Slowest
145.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
141.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
140.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (cos B) (/ x (sin B)))))
134.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
132.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity prod-diff
26×add-sqr-sqrt
24×add-cube-cbrt
18×div-inv
15×times-frac
7×add-exp-log
6×associate-/r* add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
3×associate-*r*
2×clear-num frac-2neg distribute-rgt-out-- distribute-lft-out--
1×cbrt-undiv rec-exp sub-neg flip3-- diff-log div-exp *-commutative frac-sub pow-flip flip-- associate-/l* inv-pow sub-div difference-of-squares
Calls
4 calls:
Slowest
17.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
10.0ms
(/ (* x (cos B)) (sin B))
3.0ms
(* x (cos B))
2.0ms
(/ 1 (sin B))

series315.0ms

Calls
4 calls:
Slowest
138.0ms
(/ (* x (cos B)) (sin B))
112.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
41.0ms
(* x (cos B))
24.0ms
(/ 1 (sin B))

simplify22.1s

Calls
101 calls:
Slowest
1.2s
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
1.1s
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
988.0ms
(fma (- (/ 1 (sin B))) (* x (cos B)) (* (/ 1 (sin B)) (* x (cos B))))
956.0ms
(fma (- (/ 1 (sin B))) (* x (cos B)) (* (/ 1 (sin B)) (* x (cos B))))
552.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune3.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (tan B) x))
0.2b
(/ (tan B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×prod-diff
19×add-sqr-sqrt
18×div-inv
17×add-cube-cbrt
7×associate-/r*
6×pow1 add-exp-log add-log-exp
5×associate-/r/
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u distribute-lft-out--
3×clear-num frac-2neg associate-/l*
2×rec-exp pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot frac-sub flip-- difference-of-squares associate-/l/
Calls
4 calls:
Slowest
15.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
7.0ms
(/ (tan B) x)
3.0ms
(/ 1 (/ (tan B) x))
2.0ms
(/ 1 (sin B))

series358.0ms

Calls
4 calls:
Slowest
145.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
119.0ms
(/ 1 (/ (tan B) x))
73.0ms
(/ (tan B) x)
21.0ms
(/ 1 (sin B))

simplify9.2s

Calls
75 calls:
Slowest
451.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
327.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (cbrt (/ 1 (/ (tan B) x))) (* (cbrt (/ 1 (/ (tan B) x))) (cbrt (/ 1 (/ (tan B) x)))))))
311.0ms
(fma (- (/ 1 (/ (tan B) x))) 1 (* (/ 1 (/ (tan B) x)) 1))
295.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (/ (tan B) x)) 1)))
276.0ms
(fma 1 (/ 1 (sin B)) (- (* x (/ 1 (tan B)))))

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos B) (/ (sin B) x))
0.2b
(/ (sin B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
68×*-un-lft-identity prod-diff
65×add-cube-cbrt
61×times-frac
42×div-inv
7×associate-/r* add-exp-log
6×add-cbrt-cube associate-/l* add-log-exp
5×pow1 associate-/r/
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×distribute-lft-out-- difference-of-squares
1×cbrt-undiv rec-exp sub-neg flip3-- diff-log div-exp frac-sub pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
24.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
10.0ms
(/ (cos B) (/ (sin B) x))
6.0ms
(/ (sin B) x)
2.0ms
(/ 1 (sin B))

series299.0ms

Calls
4 calls:
Slowest
127.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
94.0ms
(/ (cos B) (/ (sin B) x))
42.0ms
(/ (sin B) x)
36.0ms
(/ 1 (sin B))

simplify1.1m

Calls
197 calls:
Slowest
3.6s
(fma 1 (/ 1 (sin B)) (- (* (/ (sqrt (cos B)) (/ (sin B) x)) (/ (sqrt (cos B)) 1))))
2.1s
(fma 1 (/ 1 (sin B)) (- (* (/ (cos B) (cbrt (/ (sin B) x))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x)))))))
1.4s
(fma (- (/ (cos B) (cbrt (/ (sin B) x)))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x)))) (* (/ (cos B) (cbrt (/ (sin B) x))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x))))))
1.3s
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (cos B) (cbrt (/ (sin B) x))) (/ 1 (* (cbrt (/ (sin B) x)) (cbrt (/ (sin B) x)))))))
1.1s
(- (+ (/ B x) (* 1/120 (/ (pow B 5) x))) (* 1/6 (/ (pow B 3) x)))

prune3.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample21.9s

Algorithm
intervals
Results
8.5s1768×body1280valid
5.5s4925×body80valid
5.3s1423×body640valid
1.5s716×body320valid
757.0ms360×body160valid