Details

Time bar (total: 17.3s)

sample50.0ms

Algorithm
intervals
Results
10.0ms186×body80valid
7.0ms36×body640valid
4.0ms105×body80nan
4.0ms15×body1280valid
3.0ms13×body1280nan
2.0ms16×body640nan
1.0ms11×body320valid
1.0ms9×body320nan
1.0ms8×body160valid

simplify107.0ms

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: 17.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x y) (- 1.0 y))
2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.4b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
169×*-un-lft-identity
102×times-frac
93×prod-diff
81×add-cube-cbrt
46×difference-of-squares
44×distribute-lft-out--
8×associate-/r/
7×flip3-- flip--
6×add-exp-log log-prod
5×associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×pow1 div-inv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×log-div div-sub associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num log-pow associate--r-
Counts
3 → 187
Calls
3 calls:
24.0ms
(/ (- x y) (- 1.0 y))
55.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
52.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series212.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ (- x y) (- 1.0 y))
61.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
97.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.1s

Counts
196 → 196
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03347257
18396666
222924956
done50004113

prune484.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- 1.0 y))
0.1b
(* (- x y) (/ 1 (- 1.0 y)))
4.4b
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
4.6b
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
32×times-frac
27×add-cube-cbrt
21×associate-*r*
18×add-exp-log
11×add-cbrt-cube
8×pow1 distribute-lft-out-- difference-of-squares
6×flip3-- flip-- add-log-exp
5×associate-*l* associate-/r*
4×expm1-log1p-u div-exp prod-exp associate-/r/ log1p-expm1-u
3×log-prod fma-neg prod-diff associate-/l* unswap-sqr
2×cbrt-undiv frac-times log-div rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ rem-log-exp pow-prod-down clear-num log-pow un-div-inv *-commutative inv-pow
Counts
4 → 131
Calls
4 calls:
18.0ms
(/ 1 (- 1.0 y))
55.0ms
(* (- x y) (/ 1 (- 1.0 y)))
14.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
10.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ 1 (- 1.0 y))
62.0ms
(* (- x y) (/ 1 (- 1.0 y)))
113.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
71.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify3.1s

Counts
143 → 143
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
02221969
15141593
214391442
347801410
done50001410

prune464.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3))
0.3b
(pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3)
2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.4b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
146×add-sqr-sqrt
140×*-un-lft-identity
93×prod-diff
77×times-frac
76×add-cube-cbrt
34×difference-of-squares
32×distribute-lft-out--
14×cbrt-prod
10×pow1
8×unpow-prod-down cube-prod
6×add-exp-log log-prod associate-/r/ add-log-exp
5×flip3-- log-pow add-cbrt-cube flip--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg div-inv
2×cube-mult log-div unpow3 sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log div-sub rem-log-exp pow-exp rem-cbrt-cube associate--r- rem-cube-cbrt
Counts
4 → 185
Calls
4 calls:
3.0ms
(cbrt (pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3))
4.0ms
(pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3)
70.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
51.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(cbrt (pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3))
408.0ms
(pow (log (- 1.0 (/ (- x y) (- 1.0 y)))) 3)
70.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
114.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.9s

Counts
197 → 197
Iterations

Useful iterations: done (1.9s)

IterNodesCost
04117838
110597059
230255255
done50004417

prune517.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
1.9b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.6b
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
14.1b
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

rewrite598.0ms

Algorithm
rewrite-expression-head
Rules
1120×add-sqr-sqrt
1014×*-un-lft-identity
832×prod-diff
633×unpow-prod-down cube-prod
624×times-frac
500×add-cube-cbrt
313×difference-of-squares
259×distribute-lft-out--
111×sqr-pow
81×cube-mult unpow3
72×log-prod
48×associate-/r/
33×associate--l+
28×flip3-- flip--
24×div-inv
19×pow1
16×fma-neg
15×log-pow
6×add-exp-log add-log-exp
4×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
3×difference-cubes associate--r+
2×associate--l- sub-neg diff-log rem-log-exp
Counts
4 → 1009
Calls
4 calls:
113.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
150.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
166.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
2.0ms
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
529.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
227.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
473.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
237.0ms
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

simplify1.1s

Counts
1021 → 1021
Iterations

Useful iterations: done (967.0ms)

IterNodesCost
073171293
1175358515
done500042997

prune996.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes298.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 18.3b

bsearch164.0ms

Steps
ItersRangePoint
9
288166.37165529485
42772065132.76068
32110906.87222982
7
-2445851338.3862987
-30461436.183609415
-118579514.58451813

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02454
13239
done3239

end0.0ms

sample2.4s

Algorithm
intervals
Results
752.0ms5643×body80valid
323.0ms3746×body80nan
252.0ms840×body1280valid
225.0ms836×body640valid
120.0ms383×body640nan
120.0ms378×body1280nan
65.0ms441×body320valid
33.0ms240×body320nan
24.0ms240×body160valid
11.0ms125×body160nan