Details

sample91.0ms

Algorithm

intervals

Results

46.0ms	956×	body	80	nan
14.0ms	292×	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:

0.1b	(* (- 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)))))

rewrite45.0ms

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)))))

series544.0ms

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)))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
151.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

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

prune484.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	6	127

Merged error: 0.0b

Counts

127 → 6

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)))))

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:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
16.0ms	(* (- 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)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 9.0 (- a (/ 1.0 3.0)))
123.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
195.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	744	1046
1	3478	958
2	5001	958

prune238.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Merged error: 0.0b

Counts

115 → 5

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

rewrite78.0ms

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×	`rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 209

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)))
9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
18.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
31.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
84.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
226.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
185.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1178	2554
1	5002	2254

prune510.0ms

Filtered

221 candidates to 145 candidates (65.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	221	5	226

Merged error: 0.0b

Counts

226 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
0.3b	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
0.5b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

828×	`times-frac`
612×	`add-sqr-sqrt`
470×	`sqrt-prod`
456×	`*-un-lft-identity`
368×	`add-cube-cbrt`
203×	`associate-r`
88×	`difference-of-squares`
64×	`sqrt-div`
44×	`distribute-lft-out--`
36×	`associate-/l*`
32×	`flip3--` `flip--`
28×	`frac-times` `associate-/r/`
25×	`add-exp-log` `add-cbrt-cube`
16×	`div-inv`
15×	`associate-r/` `associate-/r`
12×	`associate-l`
11×	`pow1`
9×	`flip3-+` `flip-+`
8×	`associate-*l/`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 587

Calls

4 calls:

9.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
57.0ms	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
18.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
20.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
239.0ms	(* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
182.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
168.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (* rand (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))))))

simplify116.0ms

Algorithm

egg-herbie

Counts

599 → 599

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2001	8070
1	5002	7552

prune1.2s

Filtered

599 candidates to 325 candidates (54.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	598	1	599
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	598	6	604

Merged error: 0.0b

Counts

604 → 6

regimes106.0ms

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	17	10
1	17	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

906.0ms	27046×	body	80	nan
320.0ms	9138×	body	80	valid