Details

sample79.0ms

Algorithm

intervals

Results

14.0ms	178×	body	80	valid
11.0ms	27×	body	1280	valid
8.0ms	125×	body	80	nan
7.0ms	24×	body	640	valid
4.0ms	17×	body	320	valid
3.0ms	9×	body	1280	nan
3.0ms	13×	body	640	nan
1.0ms	10×	body	160	valid
1.0ms	6×	body	320	nan
1.0ms	4×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	2335
8	741
7	343
6	223
5	123
4	75
3	41
2	29
1	19
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite162.0ms

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×	`log-prod` `add-exp-log`
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` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `log-pow` `associate--r-`

Counts

3 → 187

Calls

3 calls:

31.0ms	(/ (- x y) (- 1.0 y))
44.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
68.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series297.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- x y) (- 1.0 y))
94.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
151.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.1s

Counts

196 → 196

Iterations

Iter	Nodes
done	5002
2	3440
1	877
0	334

prune831.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cbrt (- 1.0 y)) 3)
0.3b	(pow (cbrt (- 1.0 y)) 3)
4.7b	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
13.1b	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

rewrite7.1s

Algorithm

rewrite-expression-head

Rules

2731×	`add-sqr-sqrt`
2645×	`*-un-lft-identity`
2088×	`prod-diff`
2016×	`times-frac`
1648×	`cbrt-prod`
1464×	`unpow-prod-down` `cube-prod` `add-cube-cbrt`
622×	`difference-of-squares`
584×	`distribute-lft-out--`
222×	`sqr-pow`
209×	`cube-mult` `unpow3`
40×	`cube-div` `cbrt-div`
36×	`associate-/r/`
24×	`flip3--` `flip--`
18×	`fma-neg` `div-inv`
10×	`distribute-lft-out`
9×	`log-prod`
8×	`log-div` `frac-add`
7×	`pow1` `add-exp-log`
6×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `distribute-rgt-neg-in` `pow1/3` `pow-exp` `distribute-neg-frac` `rem-cube-cbrt`
1×	`sub-neg` `diff-log` `div-sub` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 2268

Calls

4 calls:

12.0ms	(pow (cbrt (- 1.0 y)) 3)
8.0ms	(pow (cbrt (- 1.0 y)) 3)
6.4s	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
294.0ms	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

series975.0ms

Counts

4 → 12

Calls

4 calls:

420.0ms	(pow (cbrt (- 1.0 y)) 3)
312.0ms	(pow (cbrt (- 1.0 y)) 3)
137.0ms	(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
105.0ms	(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

simplify2.1s

Counts

2280 → 2280

Iterations

Iter	Nodes
done	5001
1	3290
0	1304

prune2.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

4.7b	(log (+ (fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3)) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
12.7b	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
12.7b	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
18.9b	(fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
25×	`add-cube-cbrt`
10×	`associate-/l*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`log-prod`
2×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `fma-udef`

Counts

4 → 106

Calls

4 calls:

3.0ms	(log (+ (fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3)) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
19.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
13.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
0.0ms	(fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3))

series565.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(log (+ (fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3)) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
114.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
113.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
101.0ms	(fma (/ (- x y) (fma y (- y) (* 1.0 1.0))) (- (+ 1.0 y)) (pow (cbrt 1.0) 3))

simplify1.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1563
1	399
0	166

prune900.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

12.7b	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
12.7b	(/ (+ y (- x)) (fma (- y) y (* 1.0 1.0)))
18.9b	(fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0)
22.0b	(log (+ (expm1 (log1p (fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0))) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`times-frac`
25×	`add-cube-cbrt`
10×	`associate-/l*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-sub` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
3×	`log-prod`
2×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`
1×	`neg-sub0` `associate-+r-` `flip3--` `rem-log-exp` `unsub-neg` `log-pow` `fma-udef` `flip--`

Counts

4 → 108

Calls

4 calls:

14.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
29.0ms	(/ (+ y (- x)) (fma (- y) y (* 1.0 1.0)))
0.0ms	(fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0)
3.0ms	(log (+ (expm1 (log1p (fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0))) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- x y) (fma y (- y) (* 1.0 1.0)))
102.0ms	(/ (+ y (- x)) (fma (- y) y (* 1.0 1.0)))
76.0ms	(fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0)
163.0ms	(log (+ (expm1 (log1p (fma (/ (+ y (- x)) (fma (- y) y (* 1.0 1.0))) (+ y 1.0) 1.0))) (* (/ (- x y) (fma y (- y) (* 1.0 1.0))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2489
1	576
0	238

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes221.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.8b

bsearch290.0ms

Steps

Iters	Range		Point
10	61777.909360781356	5.507951260787393e+23	164424263.12843168
6	-531429590.62988466	-72632609.50044116	-232833485.9924947

simplify14.0ms

Iterations

Iter	Nodes
done	46
2	46
1	45
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

482.0ms	5717×	body	80	valid
352.0ms	802×	body	1280	valid
234.0ms	3676×	body	80	nan
213.0ms	786×	body	640	valid
154.0ms	336×	body	1280	nan
81.0ms	467×	body	320	valid
71.0ms	369×	body	640	nan
30.0ms	209×	body	320	nan
25.0ms	228×	body	160	valid
11.0ms	118×	body	160	nan