Details

sample67.0ms

Algorithm

intervals

Results

11.0ms	164×	body	80	valid
10.0ms	31×	body	1280	valid
6.0ms	132×	body	80	nan
6.0ms	26×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	8×	body	1280	nan
1.0ms	9×	body	320	nan
1.0ms	6×	body	640	nan
1.0ms	11×	body	160	valid
0.0ms	3×	body	160	nan

simplify131.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	54	12
5	62	12
6	70	12
7	85	12
8	103	12
9	116	12
done	116	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize15.0ms

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))
3.2b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.3b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite187.0ms

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:

44.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
26.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
49.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
54.0ms	(/ (- x y) (- 1.0 y))
82.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
97.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.1s

Counts

239 → 239

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	390	8619
1	978	7647
2	2696	5742
done	5000	4742

prune650.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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))))
3.2b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite273.0ms

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:

49.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
26.0ms	(/ (- x y) (- 1.0 y))
93.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
76.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
45.0ms	(/ (- x y) (- 1.0 y))
152.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
102.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.7s

Counts

260 → 260

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	432	8789
1	1066	8133
2	2916	6364
done	5001	5518

prune637.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite86.0ms

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:

2.0ms	(log (fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y))))
1.0ms	(fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y)))
79.0ms	(* (* 1.0 (exp 1.0)) (- x y))

series430.0ms

Counts

3 → 9

Calls

3 calls:

219.0ms	(log (fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y))))
91.0ms	(fma 1.0 (exp 1.0) (* (* 1.0 (exp 1.0)) (- x y)))
120.0ms	(* (* 1.0 (exp 1.0)) (- x y))

simplify3.9s

Counts

79 → 79

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	160	1503
1	386	1314
2	1134	1028
3	4508	982
done	5000	957

prune227.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y)))
3.3b	(fma 1.0 (/ x (pow y 2)) (/ x y))
7.6b	(/ x (pow y 2))
12.8b	(log (/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
67×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`log-prod`
14×	`associate-/r*` `difference-of-squares`
12×	`add-exp-log` `unpow-prod-down`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `rem-log-exp` `clear-num` `flip--`
1×	`pow-to-exp` `log-div` `pow-exp` `log-pow` `fma-udef`

Counts

4 → 141

Calls

4 calls:

36.0ms	(/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y)))
0.0ms	(fma 1.0 (/ x (pow y 2)) (/ x y))
9.0ms	(/ x (pow y 2))
30.0ms	(log (/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y)))
72.0ms	(fma 1.0 (/ x (pow y 2)) (/ x y))
43.0ms	(/ x (pow y 2))
154.0ms	(log (/ (exp 1.0) (- (fma 1.0 (/ x (pow y 2)) (/ x y)) (/ 1.0 y))))

simplify3.1s

Counts

153 → 153

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	269	3256
1	536	3108
2	1317	2904
3	4225	2711
done	5000	2706

prune629.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes186.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.1b

bsearch236.0ms

Steps

Iters	Range		Point
10	0.00565890190154967	3744461241692.0635	758763659.7499286
9	-534556523479.6495	-34576.49081739624	-212491914.19131115

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	57
1	28	40
done	28	40

end0.0ms

sample2.4s

Algorithm

intervals

Results

510.0ms	5726×	body	80	valid
435.0ms	360×	body	1280	nan
282.0ms	3819×	body	80	nan
276.0ms	821×	body	1280	valid
198.0ms	797×	body	640	valid
78.0ms	416×	body	640	nan
65.0ms	424×	body	320	valid
31.0ms	225×	body	320	nan
24.0ms	232×	body	160	valid
14.0ms	130×	body	160	nan