Details

sample585.0ms

Algorithm

intervals

Results

382.0ms	427×	body	80	nan
84.0ms	195×	body	10240	exit
15.0ms	237×	body	80	valid
3.0ms	21×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

34.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series156.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
44.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1331
1	413
0	171

prune511.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
28.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series398.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (exp (* 2.0 x)))
189.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)
137.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4905
2	915
1	316
0	157

prune500.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
5.4b	(log (sqrt (exp (* 2.0 x))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

22.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)
0.0ms	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
4.0ms	(log (sqrt (exp (* 2.0 x))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
22.0ms	(- (exp x) 1.0)
101.0ms	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
174.0ms	(log (sqrt (exp (* 2.0 x))))

simplify2.7s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
3	4873
2	958
1	337
0	174

prune637.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (fma 0.4999999999999998 x 1.0))
26.2b	(sqrt (+ 2.0 (* x (fma 0.4999999999999998 x 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`expm1-log1p-u` `sqrt-div` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 39

Calls

2 calls:

11.0ms	(* x (fma 0.4999999999999998 x 1.0))
8.0ms	(sqrt (+ 2.0 (* x (fma 0.4999999999999998 x 1.0))))

series232.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(* x (fma 0.4999999999999998 x 1.0))
131.0ms	(sqrt (+ 2.0 (* x (fma 0.4999999999999998 x 1.0))))

simplify1.0s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
2	946
1	244
0	103

prune181.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

78.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.4b

bsearch50.0ms

Steps

Iters	Range		Point
7	-0.00027856517442265854	-4.347642122658769e-06	-9.471958066473225e-06

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	22

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.3s	6556×	body	10240	exit
1.2s	7407×	body	80	valid
912.0ms	12569×	body	80	nan
157.0ms	716×	body	160	valid