Details

sample70.0ms

Algorithm

intervals

Results

24.0ms	76×	body	1280	valid
16.0ms	74×	body	10240	exit
9.0ms	46×	body	640	valid
4.0ms	100×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 67

Calls

2 calls:

14.0ms	(/ (exp x) (- (exp x) 1.0))
9.0ms	(- (exp x) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (exp x) (- (exp x) 1.0))
31.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	2050
2	672
1	252
0	117

prune205.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma x 1/12 (/ 1 x)) 1/2)
0.1b	(fma x 1/12 (/ 1 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+ (fma x 1/12 (/ 1 x)) 1/2)
0.0ms	(fma x 1/12 (/ 1 x))

series71.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (fma x 1/12 (/ 1 x)) 1/2)
54.0ms	(fma x 1/12 (/ 1 x))

simplify1.2s

Counts

34 → 34

Iterations

Iter	Nodes
done	5009
3	880
2	225
1	96
0	42

prune145.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))
0.0b	(exp (fma 2 x x))
0.0b	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))))
4.0b	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
49×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-cbrt-cube`
7×	`add-exp-log` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `fma-neg` `prod-diff` `fma-udef` `log1p-expm1-u`
3×	`cbrt-undiv` `exp-prod` `div-exp` `exp-sum` `associate-/l*`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `associate-/r/` `flip--` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

1.0ms	(fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))
3.0ms	(exp (fma 2 x x))
21.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))))
10.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

series279.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))
22.0ms	(exp (fma 2 x x))
144.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* (+ (exp x) 1.0) 1.0))))
46.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

simplify2.0s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1825
1	588
0	232

prune922.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))))
0.0b	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
0.0b	(exp (* x 3))
4.0b	(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
15×	`difference-cubes` `cube-unmult`
13×	`add-log-exp`
8×	`add-exp-log`
6×	`exp-lft-cube` `exp-prod` `associate-/r*` `add-cbrt-cube` `exp-to-pow`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `associate-/l*`
2×	`flip3--` `div-exp` `associate-/r/` `flip--`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `diff-log` `1-exp` `fma-udef` `div-inv` `pow-flip` `inv-pow` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

53.0ms	(/ 1 (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))))
0.0ms	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
6.0ms	(exp (* x 3))
36.0ms	(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))))
63.0ms	(fma (exp x) (exp x) (* 1.0 (+ (exp x) 1.0)))
7.0ms	(exp (* x 3))
29.0ms	(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

simplify2.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5029
3	2306
2	774
1	311
0	145

prune537.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.5b

bsearch1.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

750.0ms	2240×	body	1280	valid
727.0ms	2638×	body	10240	exit
597.0ms	828×	body	320	valid
340.0ms	1645×	body	640	valid
105.0ms	2866×	body	80	valid
33.0ms	421×	body	160	valid