Details

sample279.0ms

Algorithm

intervals

Results

136.0ms	198×	body	10240	exit
28.0ms	369×	body	80	nan
16.0ms	241×	body	80	valid
3.0ms	17×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	181	12
6	489	12
7	1695	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp x) 1.0)

rewrite159.0ms

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-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

30.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
65.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series323.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
69.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
47.0ms	(- (exp (* 2.0 x)) 1.0)
39.0ms	(- (exp x) 1.0)

simplify2.5s

Counts

167 → 167

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1071	2471
3	3554	2362
done	5000	2356

prune565.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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

rewrite56.0ms

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-exp-log` `add-cbrt-cube`
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` `sub-neg` `rem-sqrt-square` `exp-prod` `exp-to-pow` `frac-2neg` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(sqrt (exp (* 2.0 x)))
24.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
0.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
25.0ms	(- (exp x) 1.0)

series376.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (exp (* 2.0 x)))
169.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
150.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
16.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	157	1895
1	305	1270
2	672	1154
3	2175	1108
done	5000	1092

prune355.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

23.2b

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

2.0ms

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

series107.0ms

Counts

1 → 3

Calls

1 calls:

107.0ms

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

simplify2.4s

Counts

18 → 18

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	53	257
1	124	230
2	337	213
3	993	205
4	3021	200
done	5000	199

prune87.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0)))
0.5b	(* (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))) (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))))
23.2b	(sqrt (fma x (fma 0.5 x 1.0) 2.0))
23.2b	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

5.0ms	(sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0)))
41.0ms	(* (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))) (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))))
3.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))
3.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

series606.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0)))
103.0ms	(* (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))) (sqrt (sqrt (fma x (fma 0.5 x 1.0) 2.0))))
134.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))
143.0ms	(sqrt (fma x (fma 0.5 x 1.0) 2.0))

simplify2.4s

Counts

140 → 140

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	168	2917
1	361	1888
2	1016	1751
3	3168	1646
done	5000	1589

prune412.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

80% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 3.3b

bsearch39.0ms

Steps

Iters	Range		Point
8	-9.640722949014248e-05	-2.3145164395556077e-08	-3.356135868947112e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	20	31
done	20	31

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.7s	6799×	body	10240	exit
1.5s	12844×	body	80	nan
748.0ms	7436×	body	80	valid
96.0ms	687×	body	160	valid