Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	53×	body	1280	valid
6.0ms	138×	body	80	valid
5.0ms	33×	body	320	valid
4.0ms	25×	body	640	valid
1.0ms	7×	body	160	valid

simplify188.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

12.0ms	(/ x (+ x 1.0))
51.0ms	(/ (+ x 1.0) (- x 1.0))
153.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ x (+ x 1.0))
64.0ms	(/ (+ x 1.0) (- x 1.0))
179.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.7s

Counts

605 → 605

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune765.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.8b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite978.0ms

Algorithm

rewrite-expression-head

Rules

1898×	`*-un-lft-identity`
1428×	`times-frac`
1132×	`add-sqr-sqrt`
936×	`prod-diff`
810×	`add-cube-cbrt`
473×	`log-prod`
470×	`exp-sum`
365×	`distribute-lft-out`
182×	`associate-/r/`
175×	`distribute-lft-out--`
157×	`difference-of-squares`
91×	`div-inv`
55×	`flip3-+` `flip-+`
38×	`flip3--` `flip--`
18×	`fma-neg`
17×	`log-pow`
16×	`exp-prod`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 1097

Calls

4 calls:

47.0ms	(/ (+ x 1.0) (- x 1.0))
11.0ms	(/ x (+ x 1.0))
537.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
221.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (+ x 1.0) (- x 1.0))
60.0ms	(/ x (+ x 1.0))
215.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
184.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.5s

Counts

1109 → 1109

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	1136	69094
1	1825	60490
2	3748	44278
done	5000	44276

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

13.2b	(/ x (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.5b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

26.0ms	(/ x (- (* x x) (* 1.0 1.0)))
57.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
31.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
1.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ x (- (* x x) (* 1.0 1.0)))
63.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
75.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
228.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify3.1s

Counts

141 → 141

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	169	2601
1	392	2521
2	1186	2066
3	4088	1892
done	5000	1887

prune604.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

115×	`*-un-lft-identity`
60×	`times-frac`
41×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `distribute-lft-out`
18×	`fma-def`
9×	`distribute-rgt-neg-in` `associate-/r*` `distribute-lft-out--`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`associate-/r/`
5×	`difference-of-squares`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `neg-log` `frac-add` `flip--` `distribute-neg-frac`

Counts

3 → 128

Calls

3 calls:

11.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
189.0ms	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series302.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x 1.0))
75.0ms	(/ (+ x 1.0) (- x 1.0))
187.0ms	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify2.8s

Counts

137 → 137

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	181	1564
1	427	1451
2	1281	1369
3	3496	1357
done	5000	1349

prune278.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch91.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	12455.499002847031
10	-6045414056204.408	-123.41774798665298	-15309.121527086834

simplify10.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	54
1	36	39
2	47	39
3	49	39
done	49	39

end0.0ms

sample1.6s

Algorithm

intervals

Results

627.0ms	1246×	body	640	valid
427.0ms	1745×	body	1280	valid
241.0ms	4051×	body	80	valid
83.0ms	632×	body	320	valid
25.0ms	326×	body	160	valid