Details

sample39.0ms

Algorithm

intervals

Results

12.0ms	51×	body	1280	valid
7.0ms	42×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3503
6	454
5	122
4	55
3	31
2	22
1	15
0	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (pow (exp x) -2.0))
0.0b	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
0.0b	(pow (exp x) -2.0)
3.4b	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-log-exp`
6×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `unpow-prod-down` `fma-def` `associate-/l*`
2×	`difference-of-squares`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `pow-exp` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

8.0ms	(+ 1.0 (pow (exp x) -2.0))
26.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
7.0ms	(pow (exp x) -2.0)
119.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

series711.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(+ 1.0 (pow (exp x) -2.0))
138.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
140.0ms	(pow (exp x) -2.0)
260.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

simplify1.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	1623
1	511
0	214

prune609.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) -2.0)
0.0b	(/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0))))
0.2b	(* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0))
3.4b	(- (/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
85×	`times-frac` `sqrt-prod`
65×	`add-cube-cbrt`
48×	`associate-l`
39×	`prod-diff`
18×	`add-cbrt-cube` `add-exp-log`
13×	`fma-neg`
12×	`sqrt-div` `associate-/r/` `distribute-lft-out`
10×	`unswap-sqr`
7×	`pow1` `associate-/r*`
6×	`flip3-+` `associate-r` `flip-+` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow-pow` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `sqrt-undiv` `exp-prod` `unpow-prod-down`
2×	`sqrt-unprod` `associate-*l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `-commutative` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `sqr-pow` `associate-/l/`

Counts

4 → 208

Calls

4 calls:

4.0ms	(pow (exp x) -2.0)
41.0ms	(/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0))))
74.0ms	(* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0))
166.0ms	(- (/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

131.0ms	(pow (exp x) -2.0)
287.0ms	(/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0))))
353.0ms	(* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0))
292.0ms	(- (/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

simplify2.0s

Counts

220 → 220

Iterations

Iter	Nodes
done	5001
2	3333
1	717
0	285

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp -2.0) x)
0.0b	(pow (exp -2.0) x)
0.2b	(sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
3.4b	(- (sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 1.0)

rewrite926.0ms

Algorithm

rewrite-expression-head

Rules

2967×	`times-frac`
2310×	`*-un-lft-identity`
1435×	`add-sqr-sqrt`
1408×	`add-cube-cbrt`
1185×	`sqrt-prod`
717×	`prod-diff`
450×	`distribute-lft-out`
239×	`fma-neg`
142×	`associate-/r/`
80×	`div-inv`
60×	`flip3-+` `flip-+`
8×	`pow-pow`
7×	`pow1`
6×	`pow-unpow` `exp-prod` `unpow-prod-down` `add-log-exp` `difference-of-squares`
5×	`rem-sqrt-square`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`pow-to-exp` `pow-exp` `sqr-pow`
1×	`sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 1274

Calls

4 calls:

7.0ms	(pow (exp -2.0) x)
7.0ms	(pow (exp -2.0) x)
80.0ms	(sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
628.0ms	(- (sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 1.0)

series327.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (exp -2.0) x)
42.0ms	(pow (exp -2.0) x)
112.0ms	(sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
139.0ms	(- (sqrt (/ 2.0 (/ (+ 1.0 (pow (exp -2.0) x)) (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 1.0)

simplify1.8s

Counts

1286 → 1286

Iterations

Iter	Nodes
done	5001
1	2871
0	1283

prune8.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (pow (exp x) -2.0) 1.0))
0.5b	(cbrt (+ (pow (exp x) -2.0) 1.0))
0.5b	(cbrt (+ (pow (exp x) -2.0) 1.0))
30.6b	(fma (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0))) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (- 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

9.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
15.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
9.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
0.0ms	(fma (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0))) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (- 1.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

335.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
328.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
275.0ms	(cbrt (+ (pow (exp x) -2.0) 1.0))
1.2s	(fma (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0))) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (sqrt (/ (sqrt 2.0) (/ (sqrt (+ (pow (exp x) -2.0) 1.0)) (/ (sqrt 2.0) (cbrt (+ (pow (exp x) -2.0) 1.0)))))) (- 1.0))

simplify678.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	915
1	270
0	117

prune721.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.6b

bsearch199.0ms

Steps

Iters	Range		Point
9	7.46228068957284e-06	5.1212688054922095	0.0008820524827028168
9	-0.0007095347148853646	-6.590418748316962e-09	-0.0007015791518006909

simplify9.0ms

Iterations

Iter	Nodes
done	61
1	61
0	53

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	1627×	body	1280	valid
408.0ms	1289×	body	640	valid
395.0ms	4059×	body	80	valid
123.0ms	692×	body	320	valid
38.0ms	333×	body	160	valid