Details

sample16.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	81×	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	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

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:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series218.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
143.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

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

prune142.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 0b

Counts

81 → 3

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))))

rewrite35.0ms

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))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
7.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1.0))
42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
139.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
102.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (47.0ms)

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

prune175.0ms

Filtered

130 candidates to 84 candidates (64.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	130	3	133

Merged error: 0b

Counts

133 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite60.0ms

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:

5.0ms	(pow (sqrt (+ x 1.0)) 3)
11.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
21.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (sqrt (+ x 1.0)) 3)
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
196.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify148.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	825	1791
1	4123	1518
2	5001	1510

prune374.0ms

Filtered

206 candidates to 109 candidates (52.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	206	3	209

Merged error: 0b

Counts

209 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ x 1.0))
3.5b	(- (- (* 1.0 1.0) x) 1.0)
3.6b	(- 1.0 (sqrt (+ x 1.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
78×	`prod-diff`
64×	`add-cube-cbrt`
42×	`sqrt-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-l`
16×	`times-frac`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `fma-neg`
6×	`associate-r` `distribute-lft-out--`
5×	`sub-neg` `flip3--` `associate--l+` `flip--`
4×	`expm1-log1p-u` `diff-log` `log1p-expm1-u`
2×	`frac-times` `sqrt-div` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `hypot-def` `div-inv`

Counts

4 → 194

Calls

4 calls:

23.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (- (* 1.0 1.0) x) 1.0)
8.0ms	(- 1.0 (sqrt (+ x 1.0)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
30.0ms	(sqrt (+ x 1.0))
19.0ms	(- (- (* 1.0 1.0) x) 1.0)
51.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	718	2842
1	3329	2079
2	5001	1987

prune255.0ms

Filtered

206 candidates to 104 candidates (50.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	206	3	209

Merged error: 0b

Counts

209 → 3

regimes13.0ms

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

sample419.0ms

Algorithm

intervals

Results

221.0ms	7999×	body	80	valid
67.0ms	2711×	body	80	nan
0.0ms	1×	body	1280	valid