Details

sample86.0ms

Algorithm

intervals

Results

45.0ms	978×	body	80	nan
13.0ms	295×	body	80	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	10

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
80×	`times-frac`
78×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-r`
8×	`associate-*r/` `sqrt-prod` `div-inv`
6×	`sqrt-div`
4×	`expm1-log1p-u` `flip3--` `associate-/r*` `associate-/r/` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `sqrt-pow1` `div-exp` `*-commutative` `difference-of-squares`
1×	`frac-2neg` `pow1/2` `associate-*l/` `clear-num` `distribute-lft-out--`

Counts

4 → 196

Calls

4 calls:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
12.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 9.0 (- a (/ 1.0 3.0)))
180.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1057	2914
1	4158	2268
2	5001	2242

prune382.0ms

Filtered

208 candidates to 117 candidates (56.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	201	7	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	202	7	209

Merged error: 0.0b

Counts

209 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt` `prod-diff`
60×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-r`
9×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `sub-neg` `sqrt-pow1` `div-exp` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
187.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
73.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune309.0ms

Filtered

195 candidates to 103 candidates (52.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	197	5	202

Merged error: 0b

Counts

202 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
1.1b	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
139×	`add-sqr-sqrt`
134×	`*-un-lft-identity`
132×	`add-cube-cbrt`
78×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
19×	`associate-/r*`
17×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv`
9×	`pow1`
7×	`associate-/l*`
6×	`associate-r/` `associate-r*`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--`
2×	`sub-neg` `frac-2neg` `sqrt-pow1` `pow-prod-down` `clear-num` `associate-/l/` `difference-of-squares`
1×	`pow1/2` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 241

Calls

4 calls:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
10.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series447.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
151.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
183.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify67.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1278	3618
1	5001	2971

prune444.0ms

Filtered

253 candidates to 158 candidates (62.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	253	5	258

Merged error: 0b

Counts

258 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
126×	`add-sqr-sqrt`
102×	`sqrt-prod`
86×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 184

Calls

3 calls:

9.0ms	(sqrt (- a (/ 1.0 3.0)))
38.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
14.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series595.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (- a (/ 1.0 3.0)))
149.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
410.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1016	2566
1	4544	2406
2	5001	2404

prune371.0ms

Filtered

193 candidates to 124 candidates (64.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	193	5	198

Merged error: 0b

Counts

198 → 5

regimes62.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	10
1	16	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	27518×	body	80	nan
411.0ms	9121×	body	80	valid