Details

Time bar (total: 7.6m)

sample420.0ms

Algorithm
intervals
Results
107.0ms43×body1280valid
98.0ms53×body640valid
80.0ms160×body80valid
24.0ms24×body320valid
7.0ms11×body160valid

simplify187.0ms

Calls
1 calls:
Slowest
186.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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)))

rewrite58.0ms

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
Calls
3 calls:
Slowest
26.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms
(/ x (tan B))
6.0ms
(/ 1 (sin B))

series328.0ms

Calls
3 calls:
Slowest
159.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
150.0ms
(/ x (tan B))
19.0ms
(/ 1 (sin B))

simplify1.2m

Calls
456 calls:
Slowest
814.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
754.0ms
(fma (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ 1 (cbrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
630.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
572.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
561.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
107×add-sqr-sqrt
105×*-un-lft-identity
98×add-cube-cbrt
91×prod-diff
28×div-inv
15×add-exp-log
13×add-cbrt-cube fma-neg
7×pow1
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u associate-/l*
3×cbrt-undiv distribute-rgt-out-- associate-*r* associate-*l* difference-of-squares
2×clear-num frac-2neg prod-exp cbrt-unprod distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div unswap-sqr
Calls
4 calls:
Slowest
32.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
18.0ms
(/ (* x (cos B)) (sin B))
8.0ms
(* x (cos B))
6.0ms
(/ 1 (sin B))

series343.0ms

Calls
4 calls:
Slowest
147.0ms
(/ (* x (cos B)) (sin B))
123.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
40.0ms
(* x (cos B))
33.0ms
(/ 1 (sin B))

simplify40.9s

Calls
274 calls:
Slowest
579.0ms
(fma (- (/ 1 (sin B))) (* x (cos B)) (* (/ 1 (sin B)) (* x (cos B))))
528.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
457.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
420.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))
415.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

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/
Calls
4 calls:
Slowest
28.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms
(/ 1 (/ (tan B) x))
12.0ms
(/ 1 (sin B))
11.0ms
(/ (tan B) x)

series389.0ms

Calls
4 calls:
Slowest
154.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
147.0ms
(/ 1 (/ (tan B) x))
63.0ms
(/ (tan B) x)
25.0ms
(/ 1 (sin B))

simplify5.3m

Calls
1362 calls:
Slowest
897.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ 1 (/ (cbrt (tan B)) x)) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))
855.0ms
(fma (- (/ (cbrt 1) (cbrt (/ (tan B) x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (tan B) x)) (cbrt (/ (tan B) x)))) (* (/ (cbrt 1) (cbrt (/ (tan B) x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (tan B) x)) (cbrt (/ (tan B) x))))))
844.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
844.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ (cbrt 1) (/ (tan B) (cbrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt x) (cbrt x)))))))
843.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) x)) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))

prune8.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

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)))

rewrite20.0ms

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×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
12.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms
(cbrt (sin B))
2.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))

series664.0ms

Calls
4 calls:
Slowest
185.0ms
(cbrt (sin B))
168.0ms
(cbrt (sin B))
159.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
153.0ms
(cbrt (sin B))

simplify1.6s

Calls
65 calls:
Slowest
349.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
289.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
272.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
233.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
102.0ms
(* (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))) (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 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

bsearch2.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.5s1712×body1280valid
1.9s1461×body640valid
1.8s4850×body80valid
668.0ms742×body320valid
171.0ms336×body160valid