Details

Time bar (total: 6.9m)

sample412.0ms

Algorithm
intervals
Results
157.0ms60×body1280valid
68.0ms47×body640valid
49.0ms151×body80valid
23.0ms23×body320valid
9.0ms14×body160valid

simplify129.0ms

Calls
1 calls:
Slowest
129.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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)))

rewrite96.0ms

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
60.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms
(/ x (tan B))
9.0ms
(/ 1 (sin B))

series325.0ms

Calls
3 calls:
Slowest
166.0ms
(/ x (tan B))
133.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms
(/ 1 (sin B))

simplify1.2m

Calls
456 calls:
Slowest
748.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ (cbrt x) (tan B)) (/ (* (cbrt x) (cbrt x)) 1))))
606.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
584.0ms
(fma (- (/ (cbrt x) (sqrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B))) (* (/ (cbrt x) (sqrt (tan B))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B)))))
576.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
574.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
1373×times-frac
862×add-sqr-sqrt
842×*-un-lft-identity
832×add-cube-cbrt
572×prod-diff
105×div-inv
19×associate-/r*
15×add-exp-log
14×associate-/r/
13×add-cbrt-cube fma-neg
9×associate-/l* difference-of-squares
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num frac-2neg distribute-lft-out--
1×rec-exp quot-tan sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
45.0ms
(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
8.0ms
(/ (sin B) (cos B))
7.0ms
(/ x (/ (sin B) (cos B)))
5.0ms
(/ 1 (sin B))

series330.0ms

Calls
4 calls:
Slowest
151.0ms
(/ x (/ (sin B) (cos B)))
124.0ms
(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
36.0ms
(/ (sin B) (cos B))
18.0ms
(/ 1 (sin B))

simplify5.1m

Calls
1342 calls:
Slowest
937.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (/ (sin B) (cos B)))) (/ 1 (* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))))))
774.0ms
(fma (- (/ (sqrt x) (/ (sin B) (cbrt (cos B))))) (/ (sqrt x) (/ 1 (* (cbrt (cos B)) (cbrt (cos B))))) (* (/ (sqrt x) (/ (sin B) (cbrt (cos B)))) (/ (sqrt x) (/ 1 (* (cbrt (cos B)) (cbrt (cos B)))))))
761.0ms
(fma (- (/ (sqrt x) (/ (cbrt (sin B)) (sqrt (cos B))))) (/ (sqrt x) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt (cos B)))) (* (/ (sqrt x) (/ (cbrt (sin B)) (sqrt (cos B)))) (/ (sqrt x) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt (cos B))))))
737.0ms
(fma (- (/ x (/ (sqrt (sin B)) (cbrt (cos B))))) (/ 1 (/ (sqrt (sin B)) (* (cbrt (cos B)) (cbrt (cos B))))) (* (/ x (/ (sqrt (sin B)) (cbrt (cos B)))) (/ 1 (/ (sqrt (sin B)) (* (cbrt (cos B)) (cbrt (cos B)))))))
722.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (sqrt x) (/ (sqrt (sin B)) (cbrt (cos B)))) (/ (sqrt x) (/ (sqrt (sin B)) (* (cbrt (cos B)) (cbrt (cos B))))))))

prune9.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
20×times-frac
18×add-exp-log
16×associate-*l*
12×add-cbrt-cube
8×pow1
6×associate-*r* prod-diff
5×distribute-rgt-in distribute-lft-in prod-exp
4×div-exp unswap-sqr
3×expm1-log1p-u associate-/r* cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×frac-times cbrt-undiv rec-exp sub-neg flip3-- 1-exp pow-prod-down associate-*r/ *-commutative div-inv flip--
1×clear-num frac-2neg associate-*l/ pow-flip inv-pow
Calls
3 calls:
Slowest
29.0ms
(* (/ 1 (sin B)) (- 1 (* x (cos B))))
9.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series144.0ms

Calls
3 calls:
Slowest
81.0ms
(* (/ 1 (sin B)) (- 1 (* x (cos B))))
48.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify6.7s

Calls
90 calls:
Slowest
528.0ms
(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))))
375.0ms
(* 1 (- (pow 1 3) (pow (* x (cos B)) 3)))
285.0ms
(* (/ 1 (sin B)) (- (* x (cos B))))
284.0ms
(* (sin B) (+ (* 1 1) (+ (* (* x (cos B)) (* x (cos B))) (* 1 (* x (cos B))))))
283.0ms
(* (/ 1 (sin B)) (fma (- (cos B)) x (* (cos B) x)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos B) (sin B)) x)
0.2b
(/ (cos B) (sin B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))

rewrite67.0ms

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
Calls
4 calls:
Slowest
24.0ms
(* (/ (cos B) (sin B)) x)
20.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
16.0ms
(/ (cos B) (sin B))
5.0ms
(/ 1 (sin B))

series248.0ms

Calls
4 calls:
Slowest
116.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
87.0ms
(* (/ (cos B) (sin B)) x)
25.0ms
(/ 1 (sin B))
20.0ms
(/ (cos B) (sin B))

simplify6.4s

Calls
130 calls:
Slowest
594.0ms
(* (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))) (* (* x x) x))
464.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
370.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
249.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ (cos B) (sin B)) x)))
243.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* x (/ (cos B) (sin B)))))

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.5s1692×body1280valid
2.0s1450×body640valid
2.0s4912×body80valid
737.0ms718×body320valid
266.0ms358×body160valid