Details

Time bar (total: 7.6m)

sample315.0ms

Algorithm
intervals
Results
77.0ms55×body640valid
68.0ms54×body1280valid
37.0ms162×body80valid
12.0ms19×body320valid
4.0ms9×body160valid

simplify90.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
89.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))

rewrite60.0ms

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
Counts
3 → 285
Calls
3 calls:
Slowest
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
10.0ms
(/ x (tan B))
6.0ms
(/ 1 (sin B))

series331.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
168.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
135.0ms
(/ x (tan B))
27.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
572.0ms
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
570.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
566.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
560.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
559.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)))

rewrite87.0ms

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/
Counts
4 → 767
Calls
4 calls:
Slowest
37.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
9.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
5.0ms
(/ 1 (sin B))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
118.0ms
(/ 1 (/ (tan B) x))
66.0ms
(/ (tan B) x)
14.0ms
(/ 1 (sin B))

simplify5.3m

Counts
1362 → 779
Calls
1362 calls:
Slowest
902.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ 1 (/ (cbrt (tan B)) (cbrt x))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x)))))))
833.0ms
(fma (- (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x)))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))) (* (/ (sqrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (sqrt 1) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x))))))
816.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cbrt 1) (/ (sqrt (tan B)) (cbrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (tan B)) (* (cbrt x) (cbrt x)))))))
798.0ms
(fma (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ 1 (cbrt (sin B))) (- (* (/ (sqrt 1) (/ (tan B) (sqrt x))) (/ (sqrt 1) (/ 1 (sqrt x))))))
762.0ms
(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)))))

prune8.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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
Counts
4 → 208
Calls
4 calls:
Slowest
44.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
23.0ms
(/ (* x (cos B)) (sin B))
15.0ms
(* x (cos B))
10.0ms
(/ 1 (sin B))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (* x (cos B)) (sin B))
109.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
46.0ms
(* x (cos B))
23.0ms
(/ 1 (sin B))

simplify40.5s

Counts
274 → 220
Calls
274 calls:
Slowest
551.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ (cos B) (sqrt (sin B))) (/ x (sqrt (sin B))))))
468.0ms
(fma (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ 1 (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
466.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
398.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
393.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
2 → 54
Calls
2 calls:
Slowest
30.0ms
(/ (- 1 (* x (cos B))) (sin B))
15.0ms
(* x (cos B))

series146.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(/ (- 1 (* x (cos B))) (sin B))
48.0ms
(* x (cos B))

simplify2.3s

Counts
44 → 60
Calls
44 calls:
Slowest
425.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
295.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
282.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
111.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
106.0ms
(/ (- 1 (* x (cos B))) (sqrt (sin B)))

prune491.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
3.6s1763×body1280valid
2.4s1475×body640valid
2.3s4870×body80valid
698.0ms703×body320valid
287.0ms350×body160valid