Details

sample340.0ms

Algorithm

intervals

Results

152.0ms	235×	body	10240	exit
28.0ms	413×	body	80	nan
17.0ms	226×	body	80	valid
5.0ms	33×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	767
5	185
4	76
3	41
2	28
1	19
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
6.6b	(- (pow (exp 2.0) x) 1.0)
6.7b	(- (exp x) 1.0)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
71×	`times-frac`
53×	`add-cube-cbrt`
52×	`difference-of-squares`
41×	`sqrt-prod`
30×	`prod-diff`
28×	`distribute-lft-out--`
24×	`unpow-prod-down`
16×	`sqr-pow`
10×	`fma-neg`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*` `flip3--` `flip--`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 195

Calls

4 calls:

62.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
108.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
22.0ms	(- (pow (exp 2.0) x) 1.0)
13.0ms	(- (exp x) 1.0)

series370.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
106.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
72.0ms	(- (pow (exp 2.0) x) 1.0)
35.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
2	2168
1	636
0	296

prune970.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
0.0b	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
6.7b	(- (exp x) 1.0)
6.7b	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-cube-cbrt`
21×	`sqrt-prod`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `fma-udef`

Counts

4 → 112

Calls

4 calls:

26.0ms	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
25.0ms	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)
1.0ms	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

series666.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
197.0ms	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)
189.0ms	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

simplify647.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1136
1	379
0	195

prune721.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1.0 x (fma (* x x) 0.5 2.0))
25.4b	(sqrt (fma 1.0 x (fma (* x x) 0.5 2.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 25

Calls

2 calls:

0.0ms	(fma 1.0 x (fma (* x x) 0.5 2.0))
3.0ms	(sqrt (fma 1.0 x (fma (* x x) 0.5 2.0)))

series144.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(fma 1.0 x (fma (* x x) 0.5 2.0))
115.0ms	(sqrt (fma 1.0 x (fma (* x x) 0.5 2.0)))

simplify1.7s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	3679
2	554
1	145
0	64

prune115.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow (fma x (fma x 0.5 1.0) 2.0) 3)
16.7b	(cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3))
25.4b	(sqrt (cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
17×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`unpow-prod-down` `cube-prod`
5×	`pow1` `rem-sqrt-square`
4×	`add-cbrt-cube` `add-exp-log` `sqr-pow`
3×	`expm1-log1p-u` `cube-mult` `pow-unpow` `unpow3` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/3`
1×	`pow-to-exp` `pow-pow` `pow1/2` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 80

Calls

3 calls:

5.0ms	(pow (fma x (fma x 0.5 1.0) 2.0) 3)
4.0ms	(cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3))
10.0ms	(sqrt (cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(pow (fma x (fma x 0.5 1.0) 2.0) 3)
34.0ms	(cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3))
133.0ms	(sqrt (cbrt (pow (fma x (fma x 0.5 1.0) 2.0) 3)))

simplify2.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1857
1	318
0	131

prune338.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

75.7% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.1b

bsearch97.0ms

Steps

Iters	Range		Point
9	-22.455199697559465	-3.034734332568842e-06	-9.627556263318037e-06

simplify4.0ms

Iterations

Iter	Nodes
done	23
0	23

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.3s	6649×	body	10240	exit
981.0ms	12634×	body	80	nan
657.0ms	7388×	body	80	valid
109.0ms	752×	body	160	valid