Details

sample86.0ms

Algorithm

intervals

Results

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

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	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))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
17.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 9.0 (- a (/ 1.0 3.0)))
193.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
146.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	654	960
1	2527	875
2	5001	875

prune313.0ms

Filtered

122 candidates to 97 candidates (79.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0.0b

Counts

123 → 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))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
15.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
44.0ms	(* 9.0 (- a (/ 1.0 3.0)))
222.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify81.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	744	1044
1	3484	958
2	5001	958

prune244.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 0b

Counts

116 → 5

localize14.0ms

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))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac`
71×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
64×	`add-cube-cbrt`
19×	`associate-/r*`
17×	`sqrt-prod`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`associate-/l*`
6×	`associate-r/` `associate-r*` `div-inv`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
3×	`flip3--` `associate-l` `flip--`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `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 → 155

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
10.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
12.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series484.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 9.0 (- a (/ 1.0 3.0)))
175.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(/ 1.0 (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify92.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	874	1662
1	3711	1570
2	5002	1570

prune382.0ms

Filtered

167 candidates to 138 candidates (82.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	167	5	172

Merged error: 0b

Counts

172 → 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))))

rewrite67.0ms

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×	`flip3-+` `flip-+` `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 → 178

Calls

3 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
37.0ms	(* (- 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))))

series438.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt (- a (/ 1.0 3.0)))
159.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
241.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify118.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	988	2523
1	4418	2362
2	5001	2362

prune379.0ms

Filtered

187 candidates to 118 candidates (63.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Merged error: 0b

Counts

192 → 5

regimes67.0ms

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
412.0ms	9121×	body	80	valid