Details

Time bar (total: 6.9m)

sample215.0ms

Algorithm
intervals
Results
78.0ms56×body640valid
65.0ms43×body1280valid
41.0ms173×body80valid
9.0ms12×body320valid
7.0ms15×body160valid

simplify113.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
113.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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)))

rewrite60.0ms

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
33.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series276.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
149.0ms
(/ x (tan B))
112.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
15.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
642.0ms
(fma (- (/ (cbrt x) (tan B))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (tan B)) (/ (* (cbrt x) (cbrt x)) 1)))
639.0ms
(fma (- (/ (cbrt x) (cbrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B))))))
582.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
569.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
561.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

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
42.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
15.0ms
(* (/ x (sin B)) (cos B))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (sin B))

series364.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
127.0ms
(* (/ x (sin B)) (cos B))
68.0ms
(/ x (sin B))
28.0ms
(/ 1 (sin B))

simplify5.5s

Counts
130 → 154
Calls
130 calls:
Slowest
404.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
265.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
254.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (cos B) (/ x (sin B)))))
210.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
207.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize33.0ms

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)))

rewrite85.0ms

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
37.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
7.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
6.0ms
(/ 1 (sin B))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
117.0ms
(/ 1 (/ (tan B) x))
81.0ms
(/ (tan B) x)
26.0ms
(/ 1 (sin B))

simplify5.2m

Counts
1362 → 779
Calls
1362 calls:
Slowest
921.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (/ (cbrt (tan B)) x)) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))
817.0ms
(fma (- (/ (cbrt 1) (/ (sqrt (tan B)) (cbrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))) (* (/ (cbrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x))))))
809.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (sqrt 1) (/ (cbrt (tan B)) x)) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))
775.0ms
(fma (- (/ (cbrt 1) (/ (cbrt (tan B)) x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)) (* (/ (cbrt 1) (/ (cbrt (tan B)) x)) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1))))
774.0ms
(fma (- (/ 1 (/ (tan B) (sqrt x)))) (/ 1 (/ 1 (sqrt x))) (* (/ 1 (/ (tan B) (sqrt x))) (/ 1 (/ 1 (sqrt x)))))

prune7.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
47×times-frac
43×*-un-lft-identity
42×add-cube-cbrt
21×add-exp-log
14×associate-*r*
13×add-cbrt-cube fma-neg prod-diff
8×pow1
6×associate-/r* div-exp associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv rec-exp 1-exp associate-*l* unswap-sqr
2×clear-num frac-2neg tan-quot associate-*r/ associate-/r/ un-div-inv frac-sub cbrt-unprod pow-flip inv-pow
1×sub-neg flip3-- diff-log pow-prod-down *-commutative flip--
Counts
4 → 152
Calls
4 calls:
Slowest
40.0ms
(- (/ 1 (sin B)) (* x (/ 1 (tan B))))
18.0ms
(* x (/ 1 (tan B)))
6.0ms
(/ 1 (tan B))
6.0ms
(/ 1 (sin B))

series354.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(* x (/ 1 (tan B)))
140.0ms
(- (/ 1 (sin B)) (* x (/ 1 (tan B))))
39.0ms
(/ 1 (tan B))
24.0ms
(/ 1 (sin B))

simplify5.6s

Counts
140 → 164
Calls
140 calls:
Slowest
368.0ms
(* (* (* x x) x) (* (* (/ 1 (tan B)) (/ 1 (tan B))) (/ 1 (tan B))))
363.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
269.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (tan B) (tan B)) (tan B))))
223.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ 1 (tan B)))))
208.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s1723×body1280valid
2.5s1407×body640valid
1.3s4982×body80valid
639.0ms691×body320valid
188.0ms382×body160valid