Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	75×	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

localize8.0ms

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))))

series204.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(sqrt (+ x 1.0))
133.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

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

prune135.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

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))))

rewrite33.0ms

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:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
134.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
98.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (46.0ms)

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

prune168.0ms

Filtered

130 candidates to 85 candidates (65.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Merged error: 0b

Counts

134 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series479.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
215.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
84.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (+ x 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	707	1346
1	3177	1264
2	5001	1230

prune273.0ms

Filtered

106 candidates to 88 candidates (83.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0b

Counts

110 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
106×	`times-frac`
101×	`*-un-lft-identity`
72×	`sqrt-prod`
65×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 215

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
33.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series889.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
136.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
422.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
201.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	816	2726
1	4051	2397
2	5002	2228

prune323.0ms

Filtered

227 candidates to 128 candidates (56.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	227	4	231

Merged error: 0b

Counts

231 → 4

regimes15.0ms

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

sample432.0ms

Algorithm

intervals

Results

223.0ms	7997×	body	80	valid
73.0ms	2821×	body	80	nan
0.0ms	3×	body	1280	valid