Details

Time bar (total: 30.9s)

sample175.0ms

Algorithm
intervals
Results
70.0ms61×body1280valid
54.0ms58×body640valid
27.0ms148×body80valid
8.0ms14×body320valid
4.0ms9×body160valid

simplify188.0ms

Counts
1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

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
38.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms
(/ x (tan B))
6.0ms
(/ 1 (sin B))

series288.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
133.0ms
(/ x (tan B))
20.0ms
(/ 1 (sin B))

simplify838.0ms

Counts
294 → 294

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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
22.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(* x (cos B))
11.0ms
(/ (* x (cos B)) (sin B))
6.0ms
(/ 1 (sin B))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
113.0ms
(/ (* x (cos B)) (sin B))
43.0ms
(* x (cos B))
15.0ms
(/ 1 (sin B))

simplify661.0ms

Counts
220 → 220

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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

series149.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(/ (- 1 (* x (cos B))) (sin B))
51.0ms
(* x (cos B))

simplify593.0ms

Counts
60 → 60

prune486.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

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
48.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
17.0ms
(/ (tan B) x)
13.0ms
(/ 1 (/ (tan B) x))
10.0ms
(/ 1 (sin B))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ 1 (/ (tan B) x))
119.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
80.0ms
(/ (tan B) x)
14.0ms
(/ 1 (sin B))

simplify1.3s

Counts
779 → 779

prune11.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.4s

Algorithm
intervals
Results
4.1s1686×body1280valid
2.1s1483×body640valid
1.5s4864×body80valid
1.2s733×body320valid
237.0ms352×body160valid