Details

Time bar (total: 43.0s)

sample467.0ms

Algorithm
intervals
Results
428.0ms139×body80valid
13.0ms42×body1280valid
8.0ms34×body640valid
5.0ms30×body320valid
1.0ms11×body160valid

simplify365.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize26.0ms

Local error

Found 3 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
Slowest
82.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
36.0ms
(/ (+ x 1) (- x 1))
8.0ms
(/ x (+ x 1))

series208.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
127.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
42.0ms
(/ (+ x 1) (- x 1))
38.0ms
(/ x (+ x 1))

simplify1.1s

Counts
762 → 762

prune8.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
3.6b
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))
0.0b
(/ (+ 1 x) (- x 1))
0.0b
(/ x (+ 1 x))

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
2493×*-un-lft-identity
1916×times-frac
1632×add-sqr-sqrt
1224×prod-diff
1012×add-cube-cbrt
617×log-prod
614×exp-sum
487×distribute-lft-out
306×difference-of-squares
214×associate-/r/
175×distribute-lft-out--
149×difference-of-sqr-1
107×div-inv
71×flip3-+ flip-+
38×flip3-- flip--
18×fma-neg
17×log-pow
16×exp-prod
11×associate-/r*
8×add-cbrt-cube add-exp-log
7×associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num sub-neg frac-2neg div-exp associate-/l/
1×log-div exp-diff diff-log rem-log-exp frac-sub
Counts
4 → 1399
Calls
4 calls:
Slowest
168.0ms
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
65.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))
20.0ms
(/ (+ 1 x) (- x 1))
14.0ms
(/ x (+ 1 x))

series240.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
77.0ms
(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))
26.0ms
(/ x (+ 1 x))
23.0ms
(/ (+ 1 x) (- x 1))

simplify1.8s

Counts
1411 → 1411

prune15.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

30.6b
(fma (- (/ 1 (- x 1))) (+ 1 x) (* (/ 1 (- x 1)) (+ 1 x)))
8.4b
(fma 1 (/ x (+ 1 x)) (* (/ -1 (- x 1)) (+ 1 x)))
0.1b
(* (/ 1 (- x 1)) (+ 1 x))
0.1b
(* (/ -1 (- x 1)) (+ 1 x))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
54×associate-*l*
51×*-un-lft-identity
45×times-frac
28×add-cube-cbrt
18×add-exp-log
14×add-cbrt-cube
12×difference-of-squares
8×pow1 associate-*r*
6×difference-of-sqr-1 prod-exp distribute-lft-out--
5×unswap-sqr
4×expm1-log1p-u frac-times flip3-+ associate-*r/ associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×div-exp
2×distribute-rgt-in cbrt-undiv distribute-lft-in flip3-- pow-prod-down associate-*l/ *-commutative fma-udef div-inv flip-- distribute-lft-out
1×rec-exp 1-exp
Counts
4 → 137
Calls
4 calls:
Slowest
40.0ms
(* (/ 1 (- x 1)) (+ 1 x))
29.0ms
(* (/ -1 (- x 1)) (+ 1 x))
0.0ms
(fma (- (/ 1 (- x 1))) (+ 1 x) (* (/ 1 (- x 1)) (+ 1 x)))
0.0ms
(fma 1 (/ x (+ 1 x)) (* (/ -1 (- x 1)) (+ 1 x)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(fma (- (/ 1 (- x 1))) (+ 1 x) (* (/ 1 (- x 1)) (+ 1 x)))
87.0ms
(fma 1 (/ x (+ 1 x)) (* (/ -1 (- x 1)) (+ 1 x)))
30.0ms
(* (/ -1 (- x 1)) (+ 1 x))
26.0ms
(* (/ 1 (- x 1)) (+ 1 x))

simplify871.0ms

Counts
149 → 149

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

30.8b
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (+ x 1) (- (pow x 3) (pow 1 3))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3)))))
27.8b
(fma x (/ 1 (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))
12.5b
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))
12.5b
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
372×*-un-lft-identity
334×add-sqr-sqrt
284×associate-*r*
274×times-frac
192×difference-of-squares
144×unpow-prod-down cube-prod
84×add-cube-cbrt
80×sqr-pow
68×distribute-lft-out
48×distribute-lft-out--
14×add-cbrt-cube add-exp-log
8×cube-mult pow1 difference-cubes
6×associate-*l*
4×expm1-log1p-u frac-times flip3-+ associate-*l/ prod-exp associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv flip--
Counts
4 → 358
Calls
4 calls:
Slowest
159.0ms
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))
133.0ms
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))
1.0ms
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (+ x 1) (- (pow x 3) (pow 1 3))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3)))))
1.0ms
(fma x (/ 1 (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
592.0ms
(fma x (/ 1 (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))))
356.0ms
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (+ x 1) (- (pow x 3) (pow 1 3))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3)))))
76.0ms
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))
51.0ms
(* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (+ x 1) (- (pow x 3) (pow 1 3))))

simplify1.0s

Counts
370 → 370

prune6.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch205.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
803.0ms1784×body1280valid
438.0ms4048×body80valid
417.0ms1184×body640valid
174.0ms649×body320valid
49.0ms335×body160valid