Details

Time bar (total: 7.4m)

sample671.0ms

Algorithm
intervals
Results
231.0ms59×body1280valid
73.0ms44×body640valid
57.0ms157×body80valid
52.0ms16×body320valid
42.0ms12×body160valid

simplify147.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
147.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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)))

rewrite91.0ms

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
51.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms
(/ x (tan B))
11.0ms
(/ 1 (sin B))

series360.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
186.0ms
(/ x (tan B))
147.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms
(/ 1 (sin B))

simplify1.3m

Counts
504 → 294
Calls
504 calls:
Slowest
633.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
632.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
627.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
620.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))))))
619.0ms
(fma (- (/ (cbrt x) (tan B))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (tan B)) (/ (* (cbrt x) (cbrt x)) 1)))

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube fma-neg associate-*l* prod-diff
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*r* associate-*l/
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 142
Calls
4 calls:
Slowest
25.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
21.0ms
(* (/ x (sin B)) (cos B))
7.0ms
(/ x (sin B))
5.0ms
(/ 1 (sin B))

series353.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
135.0ms
(* (/ x (sin B)) (cos B))
66.0ms
(/ x (sin B))
14.0ms
(/ 1 (sin B))

simplify9.7s

Counts
190 → 154
Calls
190 calls:
Slowest
400.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
380.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))))
302.0ms
(* (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ x (sin B)) (cos B)))
270.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
251.0ms
(* (* (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B))) (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))) (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
2 → 54
Calls
2 calls:
Slowest
12.0ms
(/ (- 1 (* x (cos B))) (sin B))
7.0ms
(* x (cos B))

series148.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(/ (- 1 (* x (cos B))) (sin B))
49.0ms
(* x (cos B))

simplify4.8s

Counts
71 → 60
Calls
71 calls:
Slowest
860.0ms
(* (* (/ (- 1 (* x (cos B))) (sin B)) (/ (- 1 (* x (cos B))) (sin B))) (/ (- 1 (* x (cos B))) (sin B)))
337.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
309.0ms
(* (sin B) (+ (* 1 1) (+ (* (* x (cos B)) (* x (cos B))) (* 1 (* x (cos B))))))
301.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
245.0ms
(* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))

prune575.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

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
51.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
5.0ms
(/ 1 (sin B))

series345.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
114.0ms
(/ 1 (/ (tan B) x))
80.0ms
(/ (tan B) x)
15.0ms
(/ 1 (sin B))

simplify5.5m

Counts
1427 → 779
Calls
1427 calls:
Slowest
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)))))
875.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ 1 (/ (cbrt (tan B)) (cbrt x))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x)))))))
863.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ 1 (/ (tan B) (sqrt x))) (/ 1 (/ 1 (sqrt x))))))
742.0ms
(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)))))
737.0ms
(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)))))

prune7.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
3.4s1782×body1280valid
2.4s4886×body80valid
2.3s1402×body640valid
695.0ms701×body320valid
265.0ms363×body160valid