Details

sample140.0ms

Algorithm

intervals

Results

95.0ms	190×	body	1280	valid
12.0ms	285×	body	80	valid
9.0ms	32×	body	640	valid
5.0ms	24×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
10	2899
9	809
8	249
7	88
6	71
5	62
4	56
3	40
2	26
1	14
0	7

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ -1 (exp x))
0.0b	(- (exp x) 2.0)
2.4b	(- (- (exp x) 2.0) (/ -1 (exp x)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt` `*-un-lft-identity`
83×	`prod-diff`
73×	`add-cube-cbrt`
55×	`times-frac`
18×	`distribute-lft-out--`
17×	`difference-of-squares`
11×	`associate--l+`
10×	`add-log-exp`
8×	`fma-neg`
6×	`div-inv`
5×	`add-cbrt-cube`
4×	`diff-log` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `sub-neg` `flip3--` `log1p-expm1-u` `flip--` `associate-/l`
2×	`frac-sub`
1×	`associate--l-` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp`

Counts

3 → 160

Calls

3 calls:

11.0ms	(/ -1 (exp x))
17.0ms	(- (exp x) 2.0)
136.0ms	(- (- (exp x) 2.0) (/ -1 (exp x)))

series125.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ -1 (exp x))
28.0ms	(- (exp x) 2.0)
78.0ms	(- (- (exp x) 2.0) (/ -1 (exp x)))

simplify1.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	2591
1	644
0	262

prune809.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* x (* x x))
0.1b	(* 1/360 (* x (* x x)))
0.2b	(* 1/12 (* x x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
28×	`add-cbrt-cube` `add-exp-log`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
11×	`add-sqr-sqrt`
10×	`pow-prod-up`
8×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow2` `pow-plus` `cube-unmult` `pow-sqr`

Counts

4 → 96

Calls

4 calls:

13.0ms	(* x (* x x))
13.0ms	(* x (* x x))
34.0ms	(* 1/360 (* x (* x x)))
18.0ms	(* 1/12 (* x x))

series241.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (* x x))
66.0ms	(* x (* x x))
68.0ms	(* 1/360 (* x (* x x)))
46.0ms	(* 1/12 (* x x))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1637
1	240
0	89

prune466.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(/ (fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (- (exp x) 2.0))
5.0b	(fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
10×	`add-exp-log`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip3--` `associate-l` `associate-*l/` `flip-+` `log1p-expm1-u` `flip--`
3×	`sub-neg` `times-frac` `fma-neg` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `associate-/r` `frac-2neg` `diff-log` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

17.0ms	(- (exp x) 2.0)
26.0ms	(/ (fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
75.0ms	(* (+ (exp x) 2.0) (- (exp x) 2.0))
0.0ms	(fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1))

series592.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp x) 2.0)
398.0ms	(/ (fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
48.0ms	(* (+ (exp x) 2.0) (- (exp x) 2.0))
131.0ms	(fma (exp x) (* (+ (exp x) 2.0) (- (exp x) 2.0)) (* (+ 2.0 (exp x)) 1))

simplify2.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	3843
1	611
0	210

prune631.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 2.0 (exp x))
0.0b	(+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0)))
0.0b	(/ (fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
3.5b	(fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-*l/`
9×	`*-un-lft-identity` `add-cbrt-cube`
8×	`add-exp-log` `add-log-exp`
7×	`add-sqr-sqrt` `flip3-+` `add-cube-cbrt` `flip-+`
4×	`expm1-log1p-u` `pow1` `fma-def` `frac-add` `log1p-expm1-u`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `+-commutative` `sum-log` `div-exp` `associate-/r/` `distribute-rgt-neg-out` `distribute-lft-out`
1×	`clear-num` `associate-/r*` `frac-2neg` `unsub-neg` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 73

Calls

4 calls:

5.0ms	(+ 2.0 (exp x))
32.0ms	(+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0)))
31.0ms	(/ (fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
1.0ms	(fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1))

series420.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 2.0 (exp x))
35.0ms	(+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0)))
280.0ms	(/ (fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1)) (* (+ (exp x) 2.0) (exp x)))
96.0ms	(fma (exp x) (+ (* (+ (exp x) 2.0) (exp x)) (* (+ (exp x) 2.0) (- 2.0))) (* (+ 2.0 (exp x)) 1))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	3486
1	504
0	171

prune350.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.1s	5658×	body	1280	valid
373.0ms	1261×	body	640	valid
329.0ms	8005×	body	80	valid
89.0ms	616×	body	320	valid
31.0ms	303×	body	160	valid