Details

sample594.0ms

Algorithm

intervals

Results

343.0ms	231×	body	10240	exit
22.0ms	392×	body	80	nan
15.0ms	234×	body	80	valid
3.0ms	25×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4825
7	1216
6	342
5	135
4	66
3	38
2	27
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.3b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
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 → 155

Calls

4 calls:

37.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
12.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series250.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
112.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
27.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	3998
2	1182
1	501
0	232

prune961.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
0.2b	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
5.4b	(- (exp x) 1.0)
5.4b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 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:

32.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
26.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
17.0ms	(- (exp x) 1.0)
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series581.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
267.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
26.0ms	(- (exp x) 1.0)
131.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify2.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5065
3	3318
2	933
1	369
0	193

prune670.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma 0.5 x 1.0) 2.0)
24.3b	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

rewrite2.0ms

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 x (fma 0.5 x 1.0) 2.0)
1.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

series194.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(fma x (fma 0.5 x 1.0) 2.0)
140.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

simplify1.8s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	1393
2	414
1	145
0	64

prune191.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma 0.5 x 1.0) 2.0)
2.6b	(expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0)))
24.3b	(sqrt (expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0))))
25.4b	(log1p (fma x (fma 0.5 x 1.0) 2.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

0.0ms	(fma x (fma 0.5 x 1.0) 2.0)
0.0ms	(expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0)))
1.0ms	(sqrt (expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0))))
0.0ms	(log1p (fma x (fma 0.5 x 1.0) 2.0))

series732.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma x (fma 0.5 x 1.0) 2.0)
233.0ms	(expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0)))
333.0ms	(sqrt (expm1 (log1p (fma x (fma 0.5 x 1.0) 2.0))))
119.0ms	(log1p (fma x (fma 0.5 x 1.0) 2.0))

simplify2.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
2	1458
1	468
0	184

prune379.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes43.0ms

Accuracy

80.4% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 3.5b

bsearch74.0ms

Steps

Iters	Range		Point
7	-3.0023583529873386e-08	-9.093059953312438e-10	-2.1968944712337416e-08

simplify13.0ms

Iterations

Iter	Nodes
done	35
1	35
0	32

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.7s	6901×	body	10240	exit
1.0s	12876×	body	80	nan
947.0ms	7402×	body	80	valid
103.0ms	727×	body	160	valid