Details

Time bar (total: 28.9s)

sample306.0ms

Algorithm
intervals
Results
80.0ms55×body1280valid
69.0ms153×body80valid
52.0ms47×body640valid
12.0ms13×body320valid
9.0ms20×body160valid

simplify522.0ms

Calls
1 calls:
Slowest
522.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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)))

rewrite40.0ms

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
29.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
4.0ms
(/ x (tan B))
2.0ms
(/ 1 (sin B))

series359.0ms

Calls
3 calls:
Slowest
177.0ms
(/ x (tan B))
155.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
26.0ms
(/ 1 (sin B))

simplify3.4s

Calls
66 calls:
Slowest
126.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
116.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))
112.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))
95.0ms
(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))
95.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))

prune731.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))

rewrite32.0ms

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)))
10.0ms
(* (/ x (sin B)) (cos B))
2.0ms
(/ 1 (sin B))
1.0ms
(/ x (sin B))

series363.0ms

Calls
4 calls:
Slowest
141.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
132.0ms
(* (/ x (sin B)) (cos B))
63.0ms
(/ x (sin B))
27.0ms
(/ 1 (sin B))

simplify1.8s

Calls
43 calls:
Slowest
205.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
196.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
133.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (cos B) (/ x (sin B)))))
96.0ms
(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))
94.0ms
(fma (- (cos B)) (/ x (sin B)) (* (cos B) (/ x (sin B))))

prune897.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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
12.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
3.0ms
(/ (tan B) x)
1.0ms
(/ 1 (/ (tan B) x))
1.0ms
(/ 1 (sin B))

series350.0ms

Calls
4 calls:
Slowest
144.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
120.0ms
(/ 1 (/ (tan B) x))
62.0ms
(/ (tan B) x)
24.0ms
(/ 1 (sin B))

simplify5.1s

Calls
75 calls:
Slowest
169.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
135.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (/ (tan B) x)) 1)))
134.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* x (/ 1 (tan B)))))
130.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (/ (tan B) x)) 1)))
128.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (/ (tan B) x)) 1)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

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)))

rewrite19.0ms

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)))
2.0ms
(/ 1 (sin B))
1.0ms
(/ x (tan B))

series331.0ms

Calls
3 calls:
Slowest
158.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
147.0ms
(/ x (tan B))
26.0ms
(/ 1 (sin B))

simplify3.8s

Calls
66 calls:
Slowest
134.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
121.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (cos B) (/ x (sin B)))))
120.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
116.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))
109.0ms
(fma 1 (/ 1 (sin B)) (- (* (cos B) (/ x (sin B)))))

prune947.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
4.2s1722×body1280valid
1.9s1418×body640valid
1.5s4971×body80valid
688.0ms679×body320valid
206.0ms396×body160valid