Details

Time bar (total: 6.9m)

sample420.0ms

Algorithm
intervals
Results
141.0ms156×body80valid
130.0ms61×body1280valid
76.0ms45×body640valid
18.0ms21×body320valid
4.0ms7×body160valid

simplify105.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
104.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))

rewrite93.0ms

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
53.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
9.0ms
(/ 1 (sin B))
7.0ms
(/ x (tan B))

series479.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
284.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
179.0ms
(/ x (tan B))
16.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
679.0ms
(fma (- (/ (cbrt x) (sqrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B))) (* (/ (cbrt x) (sqrt (tan B))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B)))))
633.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ (cbrt x) (sqrt (tan B))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B))))))
609.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
599.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
592.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite114.0ms

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
46.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
5.0ms
(/ 1 (sin B))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
109.0ms
(/ 1 (/ (tan B) x))
60.0ms
(/ (tan B) x)
20.0ms
(/ 1 (sin B))

simplify5.2m

Counts
1362 → 779
Calls
1362 calls:
Slowest
915.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) x)) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))
866.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
825.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ 1 (/ (sqrt (tan B)) (sqrt x))) (/ 1 (/ (sqrt (tan B)) (sqrt x))))))
816.0ms
(fma (- (/ 1 (/ (cbrt (tan B)) (cbrt x)))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x)))) (* (/ 1 (/ (cbrt (tan B)) (cbrt x))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))))
788.0ms
(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)))))

prune7.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

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))

rewrite30.0ms

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
18.0ms
(/ 1 (sin B))
10.0ms
(/ -1 (tan B))
0.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))

series160.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
101.0ms
(fma (/ -1 (tan B)) x (/ 1 (sin B)))
44.0ms
(/ -1 (tan B))
14.0ms
(/ 1 (sin B))

simplify2.1s

Counts
62 → 85
Calls
62 calls:
Slowest
600.0ms
(/ (* (* -1 -1) -1) (* (* (tan B) (tan B)) (tan B)))
225.0ms
(- (+ (* 1/3 B) (* 1/45 (pow B 3))) (/ 1 B))
204.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
134.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
89.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune905.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite45.0ms

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
14.0ms
(/ 1 (/ (sin B) (* x (cos B))))
12.0ms
(/ (sin B) (* x (cos B)))
12.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series260.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ 1 (/ (sin B) (* x (cos B))))
83.0ms
(/ (sin B) (* x (cos B)))
50.0ms
(* x (cos B))
17.0ms
(/ 1 (sin B))

simplify5.4s

Counts
124 → 150
Calls
124 calls:
Slowest
316.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
209.0ms
(- 0 (- (log (sin B)) (+ (log x) (log (cos B)))))
207.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))))
202.0ms
(/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))))
201.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))))

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.6s1705×body1280valid
2.3s1370×body640valid
1.4s5084×body80valid
1.3s717×body320valid
228.0ms362×body160valid