Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	109×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series219.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(sqrt (+ x 1.0))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	334	508
1	1222	457
2	5002	445

prune147.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 0b

Counts

81 → 5

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `hypot-def` `inv-pow`

Counts

4 → 118

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
15.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
147.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
105.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	472	857
1	2046	741
2	5001	696

prune183.0ms

Filtered

130 candidates to 83 candidates (63.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	130	5	135

Merged error: 0b

Counts

135 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
234×	`sqrt-prod`
200×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `hypot-def` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 329

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
26.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
139.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
146.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
445.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	906	5696
1	3568	5078
2	5001	5045

prune437.0ms

Filtered

341 candidates to 152 candidates (44.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	341	5	346

Merged error: 0b

Counts

346 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

11.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
23.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
72.0ms	(pow (sqrt (+ x 1.0)) 3)
70.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
205.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify145.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	825	1791
1	4126	1518
2	5001	1510

prune398.0ms

Filtered

206 candidates to 109 candidates (52.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	206	5	211

Merged error: 0b

Counts

211 → 5

regimes45.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample414.0ms

Algorithm

intervals

Results

217.0ms	7996×	body	80	valid
71.0ms	2683×	body	80	nan
1.0ms	4×	body	1280	valid

Details

sample17.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series219.0ms

simplify38.0ms

prune147.0ms

localize6.0ms

rewrite37.0ms

series331.0ms

simplify55.0ms

prune183.0ms

localize7.0ms

rewrite68.0ms

series862.0ms

simplify117.0ms

prune437.0ms

localize15.0ms

rewrite62.0ms

series364.0ms

simplify145.0ms

prune398.0ms

regimes45.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample414.0ms

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