Details

Time bar (total: 33.4s)

sample451.0ms

Algorithm
intervals
Results
185.0ms51×body1280valid
61.0ms130×body80valid
38.0ms42×body640valid
16.0ms256×pre80true
14.0ms20×body320valid
7.0ms13×body160valid

simplify72.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(/ (* e (sin v)) (+ 1 (* e (cos v))))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b
(* e (cos v))
0.1b
(* e (sin v))
0.0b
(/ (* e (sin v)) (+ 1 (* e (cos v))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×associate-*r* associate-*l*
3×expm1-log1p-u associate-/r* times-frac prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l*
Counts
3 → 68
Calls
3 calls:
Slowest
14.0ms
(/ (* e (sin v)) (+ 1 (* e (cos v))))
10.0ms
(* e (sin v))
9.0ms
(* e (cos v))

series256.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
116.0ms
(/ (* e (sin v)) (+ 1 (* e (cos v))))
82.0ms
(* e (cos v))
58.0ms
(* e (sin v))

simplify2.8s

Counts
44 → 77
Calls
44 calls:
Slowest
460.0ms
(+ (* 1 1) (- (* (* e (cos v)) (* e (cos v))) (* 1 (* e (cos v)))))
328.0ms
(/ (* (* (* e (sin v)) (* e (sin v))) (* e (sin v))) (* (* (+ 1 (* e (cos v))) (+ 1 (* e (cos v)))) (+ 1 (* e (cos v)))))
299.0ms
(* (* (* e e) e) (* (* (cos v) (cos v)) (cos v)))
298.0ms
(/ (* (* (* e e) e) (* (* (sin v) (sin v)) (sin v))) (* (* (+ 1 (* e (cos v))) (+ 1 (* e (cos v)))) (+ 1 (* e (cos v)))))
262.0ms
(* (* (* e e) e) (* (* (sin v) (sin v)) (sin v)))

prune725.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b
(* e (/ (sin v) (fma e (cos v) 1)))
0.0b
(/ (sin v) (fma e (cos v) 1))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×times-frac
18×*-un-lft-identity add-cube-cbrt
13×associate-*r*
9×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*l* associate-/l*
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
2 → 65
Calls
2 calls:
Slowest
20.0ms
(* e (/ (sin v) (fma e (cos v) 1)))
16.0ms
(/ (sin v) (fma e (cos v) 1))

series238.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
152.0ms
(* e (/ (sin v) (fma e (cos v) 1)))
86.0ms
(/ (sin v) (fma e (cos v) 1))

simplify3.8s

Counts
56 → 71
Calls
56 calls:
Slowest
416.0ms
(- v (+ (* 1/6 (pow v 3)) (* e v)))
370.0ms
(- (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* e (cos v)))) (/ (sin v) (* (pow e 2) (pow (cos v) 2))))
325.0ms
(* (* (* e e) e) (* (* (/ (sin v) (fma e (cos v) 1)) (/ (sin v) (fma e (cos v) 1))) (/ (sin v) (fma e (cos v) 1))))
316.0ms
(- (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* e (cos v)))) (/ (sin v) (* (pow e 2) (pow (cos v) 2))))
202.0ms
(- (+ (/ (sin v) (* (pow e 2) (pow (cos v) 3))) (/ (sin v) (cos v))) (/ (sin v) (* e (pow (cos v) 2))))

prune758.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (expm1 (/ (sin v) (fma e (cos v) 1))))
0.1b
(* e (log1p (expm1 (/ (sin v) (fma e (cos v) 1)))))
0.1b
(expm1 (/ (sin v) (fma e (cos v) 1)))
0.0b
(/ (sin v) (fma e (cos v) 1))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv expm1-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
Slowest
15.0ms
(* e (log1p (expm1 (/ (sin v) (fma e (cos v) 1)))))
8.0ms
(/ (sin v) (fma e (cos v) 1))
1.0ms
(expm1 (/ (sin v) (fma e (cos v) 1)))
1.0ms
(log1p (expm1 (/ (sin v) (fma e (cos v) 1))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(* e (log1p (expm1 (/ (sin v) (fma e (cos v) 1)))))
108.0ms
(log1p (expm1 (/ (sin v) (fma e (cos v) 1))))
93.0ms
(expm1 (/ (sin v) (fma e (cos v) 1)))
61.0ms
(/ (sin v) (fma e (cos v) 1))

simplify6.5s

Counts
49 → 87
Calls
49 calls:
Slowest
872.0ms
(- (+ (* 1/6 (/ (pow (sin v) 3) (* (pow e 3) (pow (cos v) 3)))) (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (+ (/ (sin v) (* e (cos v))) (* 1/2 (/ (pow (sin v) 2) (* (pow e 2) (pow (cos v) 2))))))) (+ (/ (pow (sin v) 2) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* (pow e 2) (pow (cos v) 2)))))
776.0ms
(- (+ (* 1/6 (/ (pow (sin v) 3) (* (pow e 3) (pow (cos v) 3)))) (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (+ (/ (sin v) (* e (cos v))) (* 1/2 (/ (pow (sin v) 2) (* (pow e 2) (pow (cos v) 2))))))) (+ (/ (pow (sin v) 2) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* (pow e 2) (pow (cos v) 2)))))
485.0ms
(- v (+ (* 1/6 (pow v 3)) (* e v)))
437.0ms
(- (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* e (cos v)))) (/ (sin v) (* (pow e 2) (pow (cos v) 2))))
412.0ms
(- (+ (/ (sin v) (* (pow e 3) (pow (cos v) 3))) (/ (sin v) (* e (cos v)))) (/ (sin v) (* (pow e 2) (pow (cos v) 2))))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ e (/ (+ 1 (* e (cos v))) (sin v)))
0.2b
(/ (+ 1 (* e (cos v))) (sin v))
0.1b
(* e (cos v))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
57×add-sqr-sqrt
55×*-un-lft-identity add-cube-cbrt
16×associate-/r*
12×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv div-exp
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-/l/
1×flip3-+ pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
3 → 126
Calls
3 calls:
Slowest
49.0ms
(/ (+ 1 (* e (cos v))) (sin v))
19.0ms
(/ e (/ (+ 1 (* e (cos v))) (sin v)))
11.0ms
(* e (cos v))

series291.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(/ e (/ (+ 1 (* e (cos v))) (sin v)))
111.0ms
(/ (+ 1 (* e (cos v))) (sin v))
50.0ms
(* e (cos v))

simplify8.2s

Counts
144 → 135
Calls
144 calls:
Slowest
653.0ms
(/ (* (* e e) e) (* (* (/ (+ 1 (* e (cos v))) (sin v)) (/ (+ 1 (* e (cos v))) (sin v))) (/ (+ 1 (* e (cos v))) (sin v))))
603.0ms
(/ (* (* (+ 1 (* e (cos v))) (+ 1 (* e (cos v)))) (+ 1 (* e (cos v)))) (* (* (sin v) (sin v)) (sin v)))
307.0ms
(/ (* (cbrt e) (cbrt e)) (/ (* (cbrt (+ 1 (* e (cos v)))) (cbrt (+ 1 (* e (cos v))))) (* (cbrt (sin v)) (cbrt (sin v)))))
297.0ms
(/ (* (* e e) e) (/ (* (* (+ 1 (* e (cos v))) (+ 1 (* e (cos v)))) (+ 1 (* e (cos v)))) (* (* (sin v) (sin v)) (sin v))))
291.0ms
(* (* (* e e) e) (* (* (cos v) (cos v)) (cos v)))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.8s1478×body1280valid
1.5s1258×body640valid
1.4s4357×body80valid
427.0ms570×body320valid
347.0ms8000×pre80true
124.0ms337×body160valid