Details

Time bar (total: 20.2s)

sample55.0ms

Algorithm
intervals
Results
13.0ms180×body80valid
7.0ms28×body1280valid
5.0ms133×body80nan
5.0ms25×body640valid
3.0ms15×body1280nan
2.0ms13×body320valid
1.0ms8×body640nan
1.0ms10×body160valid
1.0ms6×body320nan
0.0ms2×body160nan

simplify136.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22912
34112
45412
56212
67012
78512
810312
911612
done11612

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b
(/ (- x y) (- 1.0 y))
2.6b
(- 1.0 (/ (- x y) (- 1.0 y)))
5.0b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
192×add-sqr-sqrt
184×*-un-lft-identity
105×prod-diff
103×times-frac
91×add-cube-cbrt
49×difference-of-squares
47×distribute-lft-out--
12×log-prod
9×pow1 flip3-- flip--
8×associate-/r/
7×add-exp-log add-log-exp
6×fma-neg add-cbrt-cube associate--r+
5×associate-/r* log-pow associate-/l*
4×expm1-log1p-u log-div log1p-expm1-u div-inv
3×associate--r-
2×sub-neg diff-log div-sub associate-/l/
1×cbrt-undiv frac-2neg div-exp rem-log-exp clear-num
Counts
4 → 227
Calls
4 calls:
72.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms
(/ (- x y) (- 1.0 y))
93.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
71.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
55.0ms
(/ (- x y) (- 1.0 y))
79.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
116.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.9s

Counts
239 → 239
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03908619
19787647
226965742
done50004742

prune518.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b
(/ (- x y) (- 1.0 y))
0.1b
(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.6b
(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
226×add-sqr-sqrt
202×*-un-lft-identity
144×times-frac
102×add-cube-cbrt
93×prod-diff
58×difference-of-squares
50×distribute-lft-out--
24×log-prod
12×associate-/r/
11×associate-/r*
9×add-exp-log
8×flip3-- add-cbrt-cube flip-- associate-/l*
6×div-inv add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×fma-neg div-exp
2×cbrt-undiv frac-2neg div-sub rem-log-exp clear-num associate-/l/
1×sub-neg log-div diff-log log-pow associate--r-
Counts
4 → 248
Calls
4 calls:
45.0ms
(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms
(/ (- x y) (- 1.0 y))
112.0ms
(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
89.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
60.0ms
(/ (- x y) (- 1.0 y))
188.0ms
(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
83.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.9s

Counts
260 → 260
Iterations

Useful iterations: done (2.9s)

IterNodesCost
04328789
110668133
229166364
done50015518

prune618.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
5.0b
(log (+ (fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3)) (* (/ (- x y) (- (pow 1.0 3) (pow y 3))) (+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y)))))))
13.3b
(+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y))))
19.7b
(fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
240×add-sqr-sqrt
160×*-un-lft-identity
125×times-frac
122×difference-of-squares
72×unpow-prod-down cube-prod
56×distribute-lft-out--
48×sqr-pow
44×add-cube-cbrt
25×associate-/r*
10×fma-def
8×add-log-exp
7×add-exp-log distribute-lft-neg-in
6×difference-cubes distribute-rgt-neg-in add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u distribute-rgt-out log1p-expm1-u distribute-lft-out
3×neg-mul-1 log-prod fma-udef
2×log-div flip3-- distribute-lft1-in flip3-+ sum-log associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-sub0 associate-+l- associate-+l+ associate-+r+ distribute-neg-in frac-2neg div-sub div-exp rem-log-exp neg-log clear-num log-pow div-inv
Counts
4 → 237
Calls
4 calls:
69.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
4.0ms
(log (+ (fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3)) (* (/ (- x y) (- (pow 1.0 3) (pow y 3))) (+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y)))))))
13.0ms
(+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y))))
0.0ms
(fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3))

series628.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
352.0ms
(log (+ (fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3)) (* (/ (- x y) (- (pow 1.0 3) (pow y 3))) (+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y)))))))
2.0ms
(+ (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (fma 1.0 1.0 (* y (+ 1.0 y))))
170.0ms
(fma (/ (- x y) (- (pow 1.0 3) (pow y 3))) (- (fma 1.0 1.0 (* y (+ 1.0 y)))) (pow (cbrt 1.0) 3))

simplify1.8s

Counts
249 → 249
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03386529
18005232
221004646
done50014483

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y)))
0.3b
(log (fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y))))
0.4b
(* (* 1.0 (exp 1.0)) (- x y))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
18×prod-diff
17×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
9×pow1
8×add-exp-log add-cbrt-cube
5×associate-*r*
3×expm1-log1p-u log-prod pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×sub-neg associate-*r/
1×flip3-- rem-log-exp associate-*l* log-pow *-commutative flip-- fma-udef distribute-lft-out-- difference-of-squares
Counts
3 → 70
Calls
3 calls:
0.0ms
(fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y)))
1.0ms
(log (fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y))))
63.0ms
(* (* 1.0 (exp 1.0)) (- x y))

series487.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y)))
270.0ms
(log (fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y))))
105.0ms
(* (* 1.0 (exp 1.0)) (- x y))

simplify4.1s

Counts
79 → 79
Iterations

Useful iterations: done (4.1s)

IterNodesCost
01601503
13861314
211341028
34516982
done5000956

prune255.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes247.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.4b

bsearch216.0ms

Steps
ItersRangePoint
8
249.10217458544693
6884452.324493753
6764068.667720944
8
-3892407191.414854
-7654410.146863867
-391848944.81012684

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
036101
14485
done4485

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s5668×body80valid
421.0ms850×body1280valid
304.0ms3716×body80nan
236.0ms769×body640valid
177.0ms443×body320valid
116.0ms352×body1280nan
94.0ms381×body640nan
41.0ms227×body320nan
37.0ms270×body160valid
14.0ms115×body160nan