Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	53×	body	1280	valid
15.0ms	42×	body	640	valid
12.0ms	130×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify175.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
2.7b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

19.0ms	(/ (+ x 1) (- x 1))
8.0ms	(/ x (+ x 1))
98.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ (+ x 1) (- x 1))
24.0ms	(/ x (+ x 1))
125.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.8s

Counts

762 → 762

Iterations

Iter	Nodes
done	5000
2	3237
1	1369
0	584

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ 1 (+ x 1))
30.0b	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
40×	`times-frac`
25×	`add-cube-cbrt`
12×	`distribute-lft-out`
11×	`associate-/r*`
10×	`difference-of-squares`
9×	`add-exp-log`
7×	`add-cbrt-cube` `associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `1-exp` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

3 → 109

Calls

3 calls:

21.0ms	(/ (+ x 1) (- x 1))
14.0ms	(/ 1 (+ x 1))
1.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

series159.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (+ x 1) (- x 1))
14.0ms	(/ 1 (+ x 1))
111.0ms	(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify2.3s

Counts

118 → 118

Iterations

Iter	Nodes
done	5026
3	2809
2	880
1	350
0	164

prune303.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (+ -1 x))
0.0b	(/ x (+ x 1))
2.7b	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))))
2.7b	(- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

1675×	`*-un-lft-identity`
1184×	`times-frac`
792×	`prod-diff`
733×	`add-sqr-sqrt`
709×	`add-cube-cbrt`
461×	`distribute-lft-out`
401×	`log-prod`
398×	`exp-sum`
166×	`associate-/r/`
84×	`flip3-+` `flip-+`
83×	`div-inv`
18×	`fma-neg` `distribute-lft-out--`
17×	`log-pow`
16×	`exp-prod`
8×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `difference-of-squares`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `div-exp` `associate-/l/`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `frac-sub` `flip--`

Counts

4 → 952

Calls

4 calls:

33.0ms	(/ (+ x 1) (+ -1 x))
15.0ms	(/ x (+ x 1))
177.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))))
81.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1) (+ -1 x))
24.0ms	(/ x (+ x 1))
122.0ms	(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))))
110.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (+ -1 x)))

simplify2.9s

Counts

964 → 964

Iterations

Iter	Nodes
done	5001
2	3642
1	1663
0	978

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))
0.3b	(/ 1 (* x x))
0.3b	(/ 1 (* x x))
5.8b	(+ (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)) (/ 1 (* x x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
20×	`pow1`
14×	`add-cbrt-cube`
12×	`*-un-lft-identity` `pow-flip`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`div-exp`
6×	`times-frac` `prod-exp` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `div-inv`
2×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod` `fma-udef` `distribute-lft-out` `inv-pow`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))
17.0ms	(/ 1 (* x x))
16.0ms	(/ 1 (* x x))
11.0ms	(+ (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)) (/ 1 (* x x)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))
30.0ms	(/ 1 (* x x))
36.0ms	(/ 1 (* x x))
40.0ms	(+ (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)) (/ 1 (* x x)))

simplify2.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
3	2958
2	709
1	240
0	95

prune304.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.6b

bsearch102.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	10135.341772312217
9	-101227.54480913779	-5.532094628653386e-05	-11906.396240974655

simplify19.0ms

Iterations

Iter	Nodes
done	37
2	37
1	34
0	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

765.0ms	1648×	body	1280	valid
412.0ms	1207×	body	640	valid
365.0ms	4189×	body	80	valid
171.0ms	624×	body	320	valid
100.0ms	332×	body	160	valid