Details

sample84.0ms

Algorithm

intervals

Results

41.0ms	914×	body	80	nan
16.0ms	283×	body	80	valid

simplify104.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
92.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
191.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
151.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune366.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Merged error: 0b

Counts

135 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.7b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 119

Calls

4 calls:

18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series587.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
149.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
167.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify79.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	787	1284
1	3157	1135
2	5002	1129

prune335.0ms

Filtered

131 candidates to 107 candidates (81.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Merged error: 0b

Counts

138 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`associate-*l/`
8×	`associate-*r/` `sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 123

Calls

4 calls:

21.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
20.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
173.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
135.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
161.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	758	1394
1	3358	1232
2	5001	1226

prune344.0ms

Filtered

135 candidates to 109 candidates (80.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Merged error: 0b

Counts

140 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.3b	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
102×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-exp-log` `sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`associate-l`
26×	`prod-exp`
17×	`div-exp`
16×	`difference-of-squares` `unswap-sqr`
14×	`cbrt-unprod`
13×	`pow1`
9×	`cbrt-undiv` `associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*l/`
6×	`frac-times`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 217

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
17.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
30.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
234.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
86.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
202.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1219	2615
1	5001	2311

prune511.0ms

Filtered

229 candidates to 153 candidates (66.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	230	4	234

Merged error: 0b

Counts

234 → 4

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	19	13
1	19	13

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	27719×	body	80	nan
421.0ms	9139×	body	80	valid