Details

Time bar (total: 28.9s)

sample190.0ms

Algorithm
intervals
Results
76.0ms57×body1280valid
56.0ms48×body640valid
31.0ms162×body80valid
13.0ms22×body320valid
3.0ms7×body160valid

simplify92.0ms

Calls
1 calls:
Slowest
92.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))

rewrite10.0ms

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
7.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
1.0ms
(/ 1 (sin B))
1.0ms
(/ x (tan B))

series215.0ms

Calls
3 calls:
Slowest
121.0ms
(/ x (tan B))
81.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms
(/ 1 (sin B))

simplify2.8s

Calls
66 calls:
Slowest
104.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ 1 (tan B)) x)))
92.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
90.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
87.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (tan B)) x)))
84.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (tan B)) 1)))

prune781.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity prod-diff
26×add-sqr-sqrt
24×add-cube-cbrt
18×div-inv
15×times-frac
7×add-exp-log
6×associate-/r* add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
3×associate-*r*
2×clear-num frac-2neg distribute-rgt-out-- distribute-lft-out--
1×cbrt-undiv rec-exp sub-neg flip3-- diff-log div-exp *-commutative frac-sub pow-flip flip-- associate-/l* inv-pow sub-div difference-of-squares
Calls
4 calls:
Slowest
8.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
5.0ms
(/ (* x (cos B)) (sin B))
1.0ms
(* x (cos B))
1.0ms
(/ 1 (sin B))

series264.0ms

Calls
4 calls:
Slowest
129.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
86.0ms
(/ (* x (cos B)) (sin B))
36.0ms
(* x (cos B))
13.0ms
(/ 1 (sin B))

simplify9.8s

Calls
101 calls:
Slowest
364.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
315.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
301.0ms
(fma (- (/ (cos B) (cbrt (sin B)))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))) (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B))))))
292.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
274.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.5b
(* (cbrt (tan B)) (cbrt (tan B)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×cbrt-div pow1/3 tan-quot
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
1.0ms
(cbrt (tan B))
1.0ms
(cbrt (tan B))
1.0ms
(cbrt (tan B))

series642.0ms

Calls
4 calls:
Slowest
183.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
155.0ms
(cbrt (tan B))
154.0ms
(cbrt (tan B))
151.0ms
(cbrt (tan B))

simplify545.0ms

Calls
48 calls:
Slowest
79.0ms
(+ (pow B 2/3) (+ (* 31/405 (pow (pow B 14) 1/3)) (* 2/9 (pow (pow B 8) 1/3))))
75.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
64.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
60.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
52.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin B))
0.6b
(cbrt (sin B))
0.6b
(cbrt (sin B))
0.5b
(* (cbrt (sin B)) (cbrt (sin B)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))

series607.0ms

Calls
4 calls:
Slowest
171.0ms
(cbrt (sin B))
167.0ms
(cbrt (sin B))
145.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
124.0ms
(cbrt (sin B))

simplify754.0ms

Calls
41 calls:
Slowest
178.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
157.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
146.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
125.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
10.0ms
(pow (pow (sin B) 2) 1/3)

prune932.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.6s1733×body1280valid
2.3s4895×body80valid
1.9s1470×body640valid
563.0ms680×body320valid
220.0ms373×body160valid