Details

sample10.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.4b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

12.4b

(/ x (+ (* x x) 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`associate-/r*`
4×	`associate-l`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

9.0ms

(/ x (+ (* x x) 1.0))

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(/ x (+ (* x x) 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	171	245
1	589	224
2	1979	217
3	5002	210

prune67.0ms

Filtered

42 candidates to 29 candidates (69.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	2	43

Merged error: 0b

Counts

43 → 2

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
12.3b	(sqrt (+ (* x x) 1.0))
12.3b	(sqrt (+ (* x x) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
50×	`sqrt-prod`
48×	`times-frac`
40×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`associate-/r*`
10×	`add-exp-log` `associate-l` `hypot-def`
8×	`pow1` `sqrt-div` `add-cbrt-cube`
6×	`associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `swap-sqr` `clear-num` `*-commutative` `div-inv` `unswap-sqr`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 156

Calls

4 calls:

10.0ms	(/ x (sqrt (+ (* x x) 1.0)))
11.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
11.0ms	(sqrt (+ (* x x) 1.0))
9.0ms	(sqrt (+ (* x x) 1.0))

series300.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ x (sqrt (+ (* x x) 1.0)))
72.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
56.0ms	(sqrt (+ (* x x) 1.0))
54.0ms	(sqrt (+ (* x x) 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	409	1113
1	1612	996
2	5001	933

prune272.0ms

Filtered

168 candidates to 101 candidates (60.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	168	2	170

Merged error: 0b

Counts

170 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.6b	(/ 1 (pow x 3))
18.3b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1427×	`add-sqr-sqrt`
1343×	`*-un-lft-identity`
1278×	`add-cube-cbrt`
1000×	`prod-diff`
743×	`unpow-prod-down`
301×	`associate-/r*`
290×	`cube-prod`
269×	`sqr-pow`
234×	`frac-sub`
99×	`associate-/l*`
92×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
33×	`frac-2neg` `clear-num`
25×	`fma-neg`
21×	`add-exp-log`
12×	`pow-flip` `div-exp`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-pow` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 1483

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))
81.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ 1 (pow x 5))
44.0ms	(/ 1 (pow x 3))
103.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify327.0ms

Algorithm

egg-herbie

Counts

1492 → 1492

Iterations

Useful iterations: 1 (59.0ms)

Iter	Nodes	Cost
0	4148	34491
1	5001	22020

prune616.0ms

Filtered

1492 candidates to 179 candidates (12.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1492	0	1492
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1492	2	1494

Merged error: 0b

Counts

1494 → 2

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch66.0ms

Steps

Iters	Range		Point
9	0.3235305135594418	1774840.6331059302	464.71461514553374
10	-85019.06990604498	-4.503960361653909e-11	-3914.142121382234

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample227.0ms

Algorithm

intervals

Results

141.0ms

8000×

body

valid