Details

Time bar (total: 24.9s)

sample54.0ms

Algorithm
intervals
Results
20.0ms59×body1280valid
10.0ms38×body640valid
8.0ms128×body80valid
4.0ms19×body320valid
1.0ms12×body160valid

simplify611.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize30.0ms

Local error

Found 2 expressions with local error:

3.4b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
1266×*-un-lft-identity
972×times-frac
831×add-sqr-sqrt
612×prod-diff
511×add-cube-cbrt
247×distribute-lft-out
158×difference-of-squares
108×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
54×div-inv
36×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
7×associate-/r*
4×add-cbrt-cube add-exp-log associate-/l* add-log-exp
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp frac-sub
Counts
2 → 717
Calls
2 calls:
Slowest
68.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
17.0ms
(/ (+ x 1) (- x 1))

series144.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
104.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
40.0ms
(/ (+ x 1) (- x 1))

simplify933.0ms

Counts
723 → 723

prune8.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

33.5b
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))
8.5b
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.1b
(* (/ 1 (- x 1)) (+ x 1))
0.1b
(* (/ 1 (- x 1)) (+ x 1))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
54×associate-*l*
52×*-un-lft-identity
46×times-frac
28×add-cube-cbrt
22×add-exp-log
14×add-cbrt-cube
12×difference-of-squares
8×pow1 associate-*r* prod-exp
6×difference-of-sqr-1 distribute-lft-out-- unswap-sqr
4×expm1-log1p-u frac-times flip3-+ div-exp associate-*r/ associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u add-log-exp
2×distribute-rgt-in cbrt-undiv rec-exp distribute-lft-in flip3-- 1-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv flip-- distribute-lft-out
Counts
4 → 140
Calls
4 calls:
Slowest
59.0ms
(* (/ 1 (- x 1)) (+ x 1))
48.0ms
(* (/ 1 (- x 1)) (+ x 1))
0.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))
0.0ms
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))
137.0ms
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
47.0ms
(* (/ 1 (- x 1)) (+ x 1))
25.0ms
(* (/ 1 (- x 1)) (+ x 1))

simplify2.0s

Counts
152 → 152

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

33.5b
(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))
8.5b
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.1b
(* (/ 1 (- x 1)) (+ x 1))
0.1b
(* (/ 1 (- x 1)) (+ x 1))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
54×associate-*l*
52×*-un-lft-identity
46×times-frac
28×add-cube-cbrt
22×add-exp-log
14×add-cbrt-cube
12×difference-of-squares
8×pow1 associate-*r* prod-exp
6×difference-of-sqr-1 distribute-lft-out-- unswap-sqr
4×expm1-log1p-u frac-times flip3-+ div-exp associate-*r/ associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u add-log-exp
2×distribute-rgt-in cbrt-undiv rec-exp distribute-lft-in flip3-- 1-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv flip-- distribute-lft-out
Counts
4 → 140
Calls
4 calls:
Slowest
47.0ms
(* (/ 1 (- x 1)) (+ x 1))
35.0ms
(* (/ 1 (- x 1)) (+ x 1))
0.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))
0.0ms
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (cbrt (* (* (* (/ 1 (- x 1)) (+ x 1)) (* (/ 1 (- x 1)) (+ x 1))) (* (/ 1 (- x 1)) (+ x 1)))))
122.0ms
(fma 1 (/ x (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
40.0ms
(* (/ 1 (- x 1)) (+ x 1))
25.0ms
(* (/ 1 (- x 1)) (+ x 1))

simplify2.2s

Counts
152 → 152

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

8.8b
(fma 3 (/ 1 (* x (* x x))) (+ (/ 1 (* x x)) (* (/ 1 x) 3)))
0.5b
(/ 1 (* x (* x x)))
0.3b
(* (/ 1 x) 3)
0.1b
(/ 1 (* x x))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×pow1
23×add-sqr-sqrt add-cbrt-cube
17×*-un-lft-identity times-frac
16×prod-exp add-cube-cbrt
14×pow-flip
13×associate-*l*
12×div-exp
6×cbrt-undiv rec-exp 1-exp pow-prod-up cbrt-unprod associate-/l*
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow2 clear-num associate-/r* frac-2neg pow-plus pow-sqr inv-pow
1×cube-unmult associate-*l/ *-commutative fma-udef
Counts
4 → 125
Calls
4 calls:
Slowest
44.0ms
(/ 1 (* x (* x x)))
23.0ms
(/ 1 (* x x))
20.0ms
(* (/ 1 x) 3)
1.0ms
(fma 3 (/ 1 (* x (* x x))) (+ (/ 1 (* x x)) (* (/ 1 x) 3)))

series139.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
48.0ms
(/ 1 (* x (* x x)))
38.0ms
(fma 3 (/ 1 (* x (* x x))) (+ (/ 1 (* x x)) (* (/ 1 x) 3)))
30.0ms
(* (/ 1 x) 3)
22.0ms
(/ 1 (* x x))

simplify1.3s

Counts
137 → 137

prune1.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes115.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch148.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
856.0ms4171×body80valid
779.0ms1681×body1280valid
500.0ms1242×body640valid
147.0ms597×body320valid
50.0ms309×body160valid