Details

sample10.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize4.0ms

Local error

Found 1 expressions with local error:

12.3b

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `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 → 31

Calls

1 calls:

12.0ms

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

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

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

simplify58.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune66.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
12.2b	(sqrt (+ (* x x) 1.0))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`associate-/r*`
10×	`add-exp-log`
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` `clear-num` `hypot-def` `div-inv`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 128

Calls

4 calls:

15.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
16.0ms	(/ x (sqrt (+ (* x x) 1.0)))
9.0ms	(sqrt (+ (* x x) 1.0))
9.0ms	(sqrt (+ (* x x) 1.0))

series286.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
121.0ms	(/ x (sqrt (+ (* x x) 1.0)))
47.0ms	(sqrt (+ (* x x) 1.0))
43.0ms	(sqrt (+ (* x x) 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	409	1002
1	1606	916
2	5001	867

prune281.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ x (sqrt (+ (* x x) 1.0)))))
0.2b	(expm1 (/ x (sqrt (+ (* x x) 1.0))))
12.2b	(sqrt (+ (* x x) 1.0))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
5×	`log1p-expm1-u`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 58

Calls

4 calls:

0.0ms	(log1p (expm1 (/ x (sqrt (+ (* x x) 1.0)))))
0.0ms	(expm1 (/ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))
9.0ms	(sqrt (+ (* x x) 1.0))

series807.0ms

Counts

4 → 12

Calls

4 calls:

550.0ms	(log1p (expm1 (/ x (sqrt (+ (* x x) 1.0)))))
167.0ms	(expm1 (/ x (sqrt (+ (* x x) 1.0))))
42.0ms	(sqrt (+ (* x x) 1.0))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	304	450
1	1077	413
2	5001	400

prune217.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
0.2b	(/ 1 (pow x 3))
0.3b	(/ 1 (pow x 5))
19.5b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1320×	`add-sqr-sqrt`
1236×	`*-un-lft-identity`
1171×	`add-cube-cbrt`
1000×	`prod-diff`
650×	`unpow-prod-down`
251×	`cube-prod`
238×	`sqr-pow`
79×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
25×	`fma-neg`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef`

Counts

4 → 1250

Calls

4 calls:

0.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
9.0ms	(/ 1 (pow x 3))
8.0ms	(/ 1 (pow x 5))
103.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
33.0ms	(/ 1 (pow x 3))
52.0ms	(/ 1 (pow x 5))
101.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify248.0ms

Algorithm

egg-herbie

Counts

1262 → 1262

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	2411	31677
1	5002	18173

prune482.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch49.0ms

Steps

Iters	Range		Point
10	0.43775957865898985	3845520655822.575	462.7532167774703
5	-980421.0572889767	-245561.44084452273	-449777.982748373

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample238.0ms

Algorithm

intervals

Results

125.0ms

8000×

body

valid