Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	138×	body	80	valid
3.0ms	33×	body	320	valid
3.0ms	25×	body	640	valid
0.0ms	7×	body	160	valid

simplify268.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	14	13
2	16	13
3	21	13
4	51	13
5	68	13
6	126	13
7	188	13
8	204	13
9	208	13
done	208	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize9.0ms

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)))

rewrite335.0ms

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:

14.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
162.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series333.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ x (+ x 1.0))
51.0ms	(/ (+ x 1.0) (- x 1.0))
230.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.9s

Counts

605 → 605

Iterations

Useful iterations: 1 (2.1s)

Iter	Nodes	Cost
0	523	34216
1	4981	26413
done	5000	26413

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))))))

rewrite104.0ms

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:

17.0ms	(/ x (- (* x x) (* 1.0 1.0)))
36.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
46.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ x (- (* x x) (* 1.0 1.0)))
53.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
52.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
268.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify3.2s

Counts

141 → 141

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	169	2601
1	1901	2153
done	5000	2025

prune571.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
6.7b	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
13.2b	(/ x (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
48×	`times-frac`
45×	`add-cube-cbrt`
44×	`prod-diff`
22×	`associate--l+`
13×	`difference-of-squares`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`associate-/l*`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`frac-sub` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `distribute-lft-out--`
3×	`sub-neg` `div-inv`
2×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-*r/` `div-exp` `clear-num` `associate-/l/`
1×	`expm1-log1p` `flip3-+` `fma-neg` `diff-log` `associate-*l/` `flip-+` `expm1-udef`

Counts

4 → 156

Calls

4 calls:

1.0ms	(expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
87.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
27.0ms	(/ x (- (* x x) (* 1.0 1.0)))
41.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
236.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
123.0ms	(/ x (- (* x x) (* 1.0 1.0)))
54.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

simplify1.2s

Counts

168 → 168

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	375	4864
done	5001	4098

prune970.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

6.7b	(log (exp (expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
6.7b	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
13.2b	(/ x (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
48×	`times-frac`
47×	`add-cube-cbrt`
44×	`prod-diff`
22×	`associate--l+`
13×	`difference-of-squares`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`associate-/l*`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`pow1` `frac-sub`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `log-prod` `exp-prod` `div-inv`
2×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-*r/` `div-exp` `clear-num` `associate-/l/`
1×	`log-div` `flip3-+` `exp-diff` `fma-neg` `diff-log` `rem-log-exp` `associate-*l/` `flip-+` `expm1-udef`

Counts

4 → 163

Calls

4 calls:

6.0ms	(log (exp (expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
87.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
27.0ms	(/ x (- (* x x) (* 1.0 1.0)))
66.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

series784.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(log (exp (expm1 (- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
271.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
132.0ms	(/ x (- (* x x) (* 1.0 1.0)))
52.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

simplify1.3s

Counts

175 → 175

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	395	5145
done	5000	4319

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch215.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	12102.1341977372
10	-6045414056204.408	-123.41774798665298	-10772.012317327612

simplify15.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	38	132
1	57	94
2	62	94
3	65	94
done	65	94

end0.0ms

sample1.5s

Algorithm

intervals

Results

538.0ms	1745×	body	1280	valid
327.0ms	1246×	body	640	valid
195.0ms	4051×	body	80	valid
92.0ms	632×	body	320	valid
86.0ms	326×	body	160	valid