Details

sample197.0ms

Algorithm

intervals

Results

58.0ms	193×	body	10240	exit
49.0ms	236×	body	80	valid
20.0ms	413×	body	80	nan
3.0ms	24×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
4.5b	(- (pow (exp 2.0) x) 1.0)
4.7b	(- (exp x) 1.0)

rewrite224.0ms

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:

99.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
46.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
39.0ms	(- (pow (exp 2.0) x) 1.0)
22.0ms	(- (exp x) 1.0)

series367.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
167.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
68.0ms	(- (pow (exp 2.0) x) 1.0)
38.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

207 → 207

Iterations

Iter	Nodes
done	5001
2	2187
1	636
0	296

prune979.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x))))
0.2b	(sqrt (* (/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x)))) (+ (exp x) 1.0)))
4.5b	(fma 1.0 (- 1.0) (exp (+ x x)))
4.5b	(- (exp (* x 2.0)) 1.0)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

45.0ms	(/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x))))
37.0ms	(sqrt (* (/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x)))) (+ (exp x) 1.0)))
1.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
22.0ms	(- (exp (* x 2.0)) 1.0)

series650.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x))))
223.0ms	(sqrt (* (/ (- (exp (* x 2.0)) 1.0) (fma 1.0 (- 1.0) (exp (+ x x)))) (+ (exp x) 1.0)))
75.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
30.0ms	(- (exp (* x 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	1796
1	472
0	195

prune778.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
0.2b	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
4.7b	(- (exp x) 1.0)
4.7b	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

rewrite58.0ms

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:

24.0ms	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
19.0ms	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
9.0ms	(- (exp x) 1.0)
0.0ms	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

series741.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0))
287.0ms	(sqrt (/ (fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0)) (- (exp x) 1.0)))
25.0ms	(- (exp x) 1.0)
177.0ms	(fma (pow (exp 2.0) (/ x 2)) (pow (exp 2.0) (/ x 2)) (- 1.0))

simplify746.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1136
1	379
0	195

prune702.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (exp x) 1.0)
4.7b	(- (exp x) 1.0)
4.7b	(- (exp x) 1.0)
4.7b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt` `prod-diff`
61×	`*-un-lft-identity`
53×	`add-cube-cbrt`
24×	`sqrt-prod`
23×	`unpow-prod-down`
16×	`fma-neg`
12×	`add-log-exp`
9×	`difference-of-squares` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--`

Counts

4 → 154

Calls

4 calls:

18.0ms	(- (exp x) 1.0)
18.0ms	(- (exp x) 1.0)
18.0ms	(- (exp x) 1.0)
36.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series147.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp x) 1.0)
20.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)
77.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify1.0s

Counts

166 → 166

Iterations

Iter	Nodes
done	5001
2	1286
1	403
0	177

prune865.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes77.0ms

Accuracy

71.8% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.9b

bsearch28.0ms

Steps

Iters	Range		Point
4	-1.2620558025192223e-10	-6.638792125712922e-11	-1.0586348953815684e-10

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	29

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.8s	6821×	body	10240	exit
1.9s	12777×	body	80	nan
583.0ms	7393×	body	80	valid
504.0ms	723×	body	160	valid