Details

Time bar (total: 7.2m)

sample251.0ms

Algorithm
intervals
Results
118.0ms61×body1280valid
58.0ms45×body640valid
40.0ms156×body80valid
19.0ms21×body320valid
4.0ms7×body160valid

simplify148.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
148.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
215×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
3 → 285
Calls
3 calls:
Slowest
50.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
7.0ms
(/ x (tan B))

series385.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
186.0ms
(/ x (tan B))
173.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
693.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))))))
596.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
584.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
565.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
558.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
1390×times-frac
881×add-sqr-sqrt
855×*-un-lft-identity
834×add-cube-cbrt
572×prod-diff
108×div-inv
21×add-exp-log
19×associate-/r*
15×difference-of-squares
14×associate-/r/
13×add-cbrt-cube fma-neg
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot frac-sub flip-- associate-/l/
Counts
4 → 767
Calls
4 calls:
Slowest
47.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
16.0ms
(/ 1 (/ (tan B) x))
12.0ms
(/ (tan B) x)
11.0ms
(/ 1 (sin B))

series354.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
109.0ms
(/ 1 (/ (tan B) x))
70.0ms
(/ (tan B) x)
14.0ms
(/ 1 (sin B))

simplify5.5m

Counts
1362 → 779
Calls
1362 calls:
Slowest
1.0s
(fma 1 (/ 1 (sin B)) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))
1.0s
(fma (- (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x)))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))) (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x)))))
854.0ms
(fma (- (/ (cbrt 1) (/ (tan B) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x))) (* (/ (cbrt 1) (/ (tan B) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt x)))))
837.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
739.0ms
(fma (- (/ (cbrt 1) (/ (sqrt (tan B)) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (sqrt x))) (* (/ (cbrt 1) (/ (sqrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (sqrt x)))))

prune8.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg div-inv
1×rec-exp 1-exp tan-quot associate-/r/ fma-udef pow-flip inv-pow
Counts
3 → 76
Calls
3 calls:
Slowest
5.0ms
(/ 1 (sin B))
5.0ms
(/ -1 (tan B))
0.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
149.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))
38.0ms
(/ -1 (tan B))
26.0ms
(/ 1 (sin B))

simplify2.2s

Counts
62 → 85
Calls
62 calls:
Slowest
713.0ms
(/ (* (* -1 -1) -1) (* (* (tan B) (tan B)) (tan B)))
204.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
180.0ms
(- (+ (* 1/3 B) (* 1/45 (pow B 3))) (/ 1 B))
126.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
89.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (sin B) (* x (cos B))))
0.2b
(/ (sin B) (* x (cos B)))
0.2b
(* x (cos B))
0.1b
(/ 1 (sin B))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
36×add-exp-log
34×add-sqr-sqrt
32×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube
16×div-exp
11×associate-/r*
9×associate-/l*
8×pow1 cbrt-undiv
7×div-inv
5×prod-exp
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l* cbrt-unprod
2×pow-flip inv-pow
1×pow-prod-down associate-/r/ *-commutative unswap-sqr
Counts
4 → 138
Calls
4 calls:
Slowest
15.0ms
(/ (sin B) (* x (cos B)))
14.0ms
(/ 1 (/ (sin B) (* x (cos B))))
11.0ms
(/ 1 (sin B))
7.0ms
(* x (cos B))

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(/ 1 (/ (sin B) (* x (cos B))))
88.0ms
(/ (sin B) (* x (cos B)))
84.0ms
(* x (cos B))
19.0ms
(/ 1 (sin B))

simplify5.9s

Counts
124 → 150
Calls
124 calls:
Slowest
279.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
256.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
229.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))))
228.0ms
(- 0 (- (log (sin B)) (+ (log x) (log (cos B)))))
222.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))))

prune1.7s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
3.7s1705×body1280valid
2.4s1370×body640valid
2.0s5084×body80valid
624.0ms717×body320valid
225.0ms362×body160valid