Details

sample64.0ms

Algorithm

intervals

Results

20.0ms	51×	body	1280	valid
12.0ms	42×	body	640	valid
7.0ms	129×	body	80	valid
3.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize14.0ms

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)

rewrite253.0ms

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:

17.0ms	(+ 1.0 (pow (exp x) -2.0))
34.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
7.0ms	(pow (exp x) -2.0)
182.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

series755.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(+ 1.0 (pow (exp x) -2.0))
177.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
132.0ms	(pow (exp x) -2.0)
278.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

simplify1.6s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	1623
1	511
0	214

prune738.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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)

rewrite321.0ms

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:

8.0ms	(pow (exp x) -2.0)
48.0ms	(/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0))))
70.0ms	(* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0))
176.0ms	(- (/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

series937.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (exp x) -2.0)
258.0ms	(/ (* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0)) (sqrt (+ 1.0 (pow (exp x) -2.0))))
259.0ms	(* (/ (sqrt 2.0) (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt 2.0))
310.0ms	(- (/ (* (/ (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

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
0.0b	(pow (exp -2.0) x)
0.5b	(/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))
30.5b	(- (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
56×	`add-exp-log`
46×	`add-cbrt-cube` `sqrt-prod`
45×	`times-frac`
44×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
39×	`prod-diff`
24×	`cbrt-undiv` `div-exp`
17×	`associate-/r*`
16×	`prod-exp` `cbrt-unprod`
14×	`sqrt-div`
13×	`fma-neg`
12×	`associate-/r/`
8×	`distribute-lft-out`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `unpow-prod-down` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/l*`
1×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l/` `pow-exp` `associate-r/` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 181

Calls

4 calls:

144.0ms	(/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
4.0ms	(pow (exp -2.0) x)
29.0ms	(/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))
251.0ms	(- (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

series1.7s

Counts

4 → 12

Calls

4 calls:

500.0ms	(/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
36.0ms	(pow (exp -2.0) x)
637.0ms	(/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))
540.0ms	(- (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0))))) (/ (* (sqrt 2.0) (cbrt (sqrt 2.0))) (sqrt (sqrt (+ 1.0 (pow (exp -2.0) x)))))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

simplify587.0ms

Counts

193 → 193

Iterations

Iter	Nodes
done	5000
1	1019
0	363

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize167.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
0.5b	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
0.5b	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
30.4b	(- (pow (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) (* (cbrt (sqrt 2.0)) (sqrt 2.0))) (* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))) 3) (pow 1.0 3))

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

696×	`sqrt-div`
384×	`prod-diff`
277×	`unpow-prod-down` `cube-prod`
235×	`add-sqr-sqrt`
208×	`associate-/r/`
179×	`*-un-lft-identity`
174×	`flip3-+` `flip-+`
157×	`add-cube-cbrt`
120×	`sqrt-prod`
116×	`frac-times`
58×	`associate-l/` `associate-r/`
53×	`sqr-pow`
45×	`cube-mult` `unpow3`
32×	`fma-neg`
30×	`associate-r` `associate-l`
27×	`unswap-sqr`
26×	`times-frac` `div-inv`
24×	`sqrt-pow1`
22×	`pow1`
16×	`difference-of-squares`
15×	`pow-prod-down`
12×	`pow1/2`
10×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-lft-out` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 617

Calls

4 calls:

132.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
100.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
132.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
254.0ms	(- (pow (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) (* (cbrt (sqrt 2.0)) (sqrt 2.0))) (* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))) 3) (pow 1.0 3))

series883.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
153.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
174.0ms	(* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))
407.0ms	(- (pow (/ (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) (* (cbrt (sqrt 2.0)) (sqrt 2.0))) (* (sqrt (sqrt (+ (pow (exp x) -2.0) 1.0))) (sqrt (sqrt (+ 1.0 (pow (exp x) -2.0)))))) 3) (pow 1.0 3))

simplify818.0ms

Counts

629 → 629

Iterations

Iter	Nodes
done	5001
1	1176
0	454

prune3.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes227.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.1b

bsearch239.0ms

Steps

Iters	Range		Point
9	7.46228068957284e-06	5.1212688054922095	0.0009557681698529544
9	-0.0007095347148853646	-6.590418748316962e-09	-0.0007015791518006909

simplify12.0ms

Iterations

Iter	Nodes
done	78
2	78
1	75
0	66

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	1627×	body	1280	valid
389.0ms	1289×	body	640	valid
276.0ms	4059×	body	80	valid
226.0ms	692×	body	320	valid
42.0ms	333×	body	160	valid