Details

Time bar (total: 6.9m)

sample188.0ms

Algorithm
intervals
Results
59.0ms43×body1280valid
50.0ms53×body640valid
47.0ms160×body80valid
15.0ms24×body320valid
5.0ms11×body160valid

simplify109.0ms

Calls
1 calls:
Slowest
109.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize402.0ms

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
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
25.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series300.0ms

Calls
3 calls:
Slowest
148.0ms
(/ x (tan B))
132.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
20.0ms
(/ 1 (sin B))

simplify1.1m

Calls
456 calls:
Slowest
715.0ms
(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))))))
572.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
552.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
551.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
551.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))

rewrite76.0ms

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
28.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
24.0ms
(/ (* x (cos B)) (sin B))
12.0ms
(* x (cos B))
7.0ms
(/ 1 (sin B))

series370.0ms

Calls
4 calls:
Slowest
177.0ms
(/ (* x (cos B)) (sin B))
119.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
56.0ms
(* x (cos B))
19.0ms
(/ 1 (sin B))

simplify40.5s

Calls
274 calls:
Slowest
644.0ms
(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))))))
470.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
451.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
408.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
398.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ (cos B) (cbrt (sin B))) (/ x (* (cbrt (sin B)) (cbrt (sin B)))))))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

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)))

rewrite101.0ms

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
22.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms
(/ 1 (/ (tan B) x))
10.0ms
(/ 1 (sin B))
10.0ms
(/ (tan B) x)

series336.0ms

Calls
4 calls:
Slowest
124.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
114.0ms
(/ 1 (/ (tan B) x))
72.0ms
(/ (tan B) x)
25.0ms
(/ 1 (sin B))

simplify4.7m

Calls
1362 calls:
Slowest
1.1s
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))
786.0ms
(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))))))
740.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (sqrt 1) (/ (cbrt (tan B)) x)) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) 1)))))
701.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))
691.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))

prune5.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

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)))

rewrite16.0ms

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
11.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
2.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))

series457.0ms

Calls
4 calls:
Slowest
123.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
113.0ms
(cbrt (sin B))
111.0ms
(cbrt (sin B))
110.0ms
(cbrt (sin B))

simplify1.2s

Calls
65 calls:
Slowest
200.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
200.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
196.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
184.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
64.0ms
(* (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))) (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))))

prune866.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.5s1712×body1280valid
1.8s1461×body640valid
1.5s4850×body80valid
529.0ms742×body320valid
155.0ms336×body160valid