Details

sample63.0ms

Algorithm

intervals

Results

29.0ms	917×	body	80	nan
10.0ms	298×	body	80	valid

simplify91.0ms

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

localize13.0ms

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

rewrite46.0ms

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×	`frac-times` `associate-/r*` `associate-/r/` `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 → 114

Calls

4 calls:

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

series552.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
96.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
184.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5002	1238

prune376.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Merged error: 0.0b

Counts

127 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite49.0ms

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:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
12.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
249.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
196.0ms	(/ (* 1.0 rand) (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	1046
1	3478	958
2	5001	958

prune269.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 0.0b

Counts

119 → 10

localize12.0ms

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))))
0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
61×	`associate-l`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
34×	`add-cbrt-cube`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-r`
6×	`associate-*l/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 191

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))))
15.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
12.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
19.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series619.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
149.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
78.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
217.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify52.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1086	2160
1	5001	1926

prune511.0ms

Filtered

203 candidates to 144 candidates (70.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	6	2	8
Picked	1	0	1
Done	1	0	1
Total	208	5	213

Merged error: 0.0b

Counts

213 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.2b	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
8.9b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
70×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
44×	`add-cube-cbrt`
39×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`flip3--` `flip--`
5×	`associate-/l/`
4×	`frac-times` `sqrt-div` `associate-r` `pow-prod-down` `associate-/r/` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`

Counts

4 → 170

Calls

4 calls:

15.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
21.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
21.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series548.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
187.0ms	(/ (* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)) (sqrt 9.0))
86.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
123.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify95.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	906	1837
1	3841	1609
2	5001	1588

prune428.0ms

Filtered

182 candidates to 128 candidates (70.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	182	5	187

Merged error: 0.0b

Counts

187 → 5

regimes71.0ms

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	19	14
1	19	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

869.0ms	27038×	body	80	nan
316.0ms	9182×	body	80	valid