Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	70×	body	1280	valid
6.0ms	54×	body	640	valid
5.0ms	202×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

14.0ms

(- (exp x) 1.0)

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(- (exp x) 1.0)

simplify3.4s

Counts

31 → 31

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	66	376
1	142	288
2	272	231
3	799	204
4	2411	175
done	5001	175

prune72.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 2) (fma x 1/6 1/2) x)
0.1b	(fma x 1/6 1/2)
3.8b	(/ (fma (pow x 2) (fma x 1/6 1/2) x) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
0.0ms	(fma x 1/6 1/2)
7.0ms	(/ (fma (pow x 2) (fma x 1/6 1/2) x) x)

series115.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
35.0ms	(fma x 1/6 1/2)
50.0ms	(/ (fma (pow x 2) (fma x 1/6 1/2) x) x)

simplify1.4s

Counts

58 → 58

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	84	809
1	147	783
2	344	709
3	1062	706
done	5001	703

prune208.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
17×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`exp-sum`
7×	`distribute-lft-out` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`fma-neg` `prod-diff` `associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 89

Calls

3 calls:

9.0ms	(+ 1.0 (exp x))
185.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
80.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series96.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp x))
57.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

98 → 98

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	147	1493
1	354	1441
2	995	1308
3	3234	1293
done	5000	1287

prune291.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x))))
0.0b	(* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x)))
0.0b	(* (exp (+ x x)) (exp (+ x x)))
3.0b	(- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite920.0ms

Algorithm

rewrite-expression-head

Rules

116×	`exp-prod`
90×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
31×	`distribute-lft-out`
24×	`distribute-rgt-out` `pow-prod-down`
19×	`pow-sqr` `pow-prod-up`
14×	`distribute-lft1-in` `distribute-rgt1-in`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
10×	`count-2`
8×	`associate-r` `exp-sum`
7×	`associate-l`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `times-frac` `associate-r/` `swap-sqr` `log1p-expm1-u` `associate-/l`
3×	`prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 163

Calls

4 calls:

479.0ms	(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x))))
51.0ms	(* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x)))
209.0ms	(* (exp (+ x x)) (exp (+ x x)))
170.0ms	(- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x))))
84.0ms	(* (fma 1.0 1.0 (exp (* 2 x))) (+ 1.0 (exp x)))
37.0ms	(* (exp (+ x x)) (exp (+ x x)))
40.0ms	(- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify1.6s

Counts

175 → 175

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	219	3011
1	574	2379
2	2280	1806
done	5001	1792

prune672.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch59.0ms

Steps

Iters	Range		Point
9	-108.06719872485291	-1.20447477858732e-06	-0.0001470771277477194

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	47
1	29	47
done	29	47

end0.0ms

sample2.3s

Algorithm

intervals

Results

747.0ms	2262×	body	1280	valid
656.0ms	5539×	body	80	valid
465.0ms	1670×	body	640	valid
102.0ms	781×	body	320	valid
38.0ms	447×	body	160	valid