Details

Time bar (total: 29.9s)

sample275.0ms

Algorithm
intervals
Results
93.0ms51×body640valid
84.0ms48×body1280valid
42.0ms155×body80valid
24.0ms28×body320valid
15.0ms12×body160valid

simplify83.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
83.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
27×times-frac
19×add-cube-cbrt
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×div-exp insert-posit16 div-inv distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp tan-quot associate-/r/ frac-sub pow-flip flip-- inv-pow
Counts
3 → 84
Calls
3 calls:
Slowest
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series306.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
167.0ms
(/ x (tan B))
123.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
16.0ms
(/ 1 (sin B))

simplify4.5s

Counts
121 → 93
Calls
121 calls:
Slowest
481.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
461.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
354.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (/ x (tan B)) (/ x (tan B))) (* (/ 1 (sin B)) (/ x (tan B)))))
293.0ms
(- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))
285.0ms
(- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B))))

prune863.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube associate-*l*
7×pow1
6×associate-/r* associate-/l* add-log-exp
4×div-exp insert-posit16
3×cbrt-undiv associate-*r* associate-*l/ div-inv
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 → 108
Calls
4 calls:
Slowest
28.0ms
(* (/ x (sin B)) (cos B))
24.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
7.0ms
(/ x (sin B))
5.0ms
(/ 1 (sin B))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(* (/ x (sin B)) (cos B))
120.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
55.0ms
(/ x (sin B))
19.0ms
(/ 1 (sin B))

simplify6.5s

Counts
143 → 120
Calls
143 calls:
Slowest
443.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
406.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
351.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))))
351.0ms
(/ (sqrt x) (* (cbrt (sin B)) (cbrt (sin B))))
308.0ms
(exp (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B))))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
Slowest
23.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms
(cbrt (sin B))
3.0ms
(cbrt (sin B))
2.0ms
(cbrt (sin B))

series536.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(cbrt (sin B))
138.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
135.0ms
(cbrt (sin B))
125.0ms
(cbrt (sin B))

simplify2.1s

Counts
103 → 89
Calls
103 calls:
Slowest
266.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
265.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
244.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
243.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
202.0ms
(* (* (* (cbrt (sin B)) (cbrt (sin B))) (* (cbrt (sin B)) (cbrt (sin B)))) (* (cbrt (sin B)) (cbrt (sin B))))

prune947.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

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 x)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 add-log-exp
3×cbrt-div tan-quot
Counts
4 → 51
Calls
4 calls:
Slowest
4.0ms
(cbrt (tan B))
3.0ms
(cbrt (tan B))
3.0ms
(cbrt (tan B))
1.0ms
(cbrt x)

series751.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(cbrt x)
193.0ms
(cbrt (tan B))
166.0ms
(cbrt (tan B))
131.0ms
(cbrt (tan B))

simplify1.6s

Counts
74 → 63
Calls
74 calls:
Slowest
201.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
193.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
193.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
162.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
68.0ms
(* (* (cbrt (tan B)) (cbrt (tan B))) (cbrt (tan B)))

prune852.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch6.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.6s1732×body1280valid
2.2s1393×body640valid
1.4s4897×body80valid
773.0ms733×body320valid
267.0ms380×body160valid