Details

sample82.0ms

Algorithm

intervals

Results

41.0ms	888×	body	80	nan
14.0ms	302×	body	80	valid

simplify95.0ms

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

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

rewrite43.0ms

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

series534.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
188.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3609	1238
2	5001	1238

prune324.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Merged error: 0b

Counts

127 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.9b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite52.0ms

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×	`associate-r` `associate-/r*` `associate-/r/` `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 → 111

Calls

4 calls:

7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series576.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
150.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
193.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
162.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify82.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	754	1232
1	3051	1085
2	5002	1085

prune294.0ms

Filtered

123 candidates to 99 candidates (80.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Merged error: 0b

Counts

128 → 5

localize11.0ms

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

rewrite50.0ms

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)))
19.0ms	(* (- 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))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 9.0 (- a (/ 1.0 3.0)))
161.0ms	(* (- 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))))
197.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (18.0ms)

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

prune234.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	109	5	114

Merged error: 0b

Counts

114 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-l`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
13×	`sqrt-prod`
12×	`pow1`
8×	`times-frac` `associate-*r/`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3--` `sqrt-div` `flip--` `unswap-sqr`
5×	`pow-prod-down`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate-/r/` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `associate-l/` `-commutative` `flip-+` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out--`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `clear-num` `associate-/r*`

Counts

4 → 118

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
15.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
14.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
11.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series688.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)))
196.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
239.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
91.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify112.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	846	1427
1	4130	1300
2	5001	1296

prune282.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	130	5	135

Merged error: 0b

Counts

135 → 5

regimes65.0ms

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

sample2.2s

Algorithm

intervals

Results

1.2s	27362×	body	80	nan
411.0ms	9121×	body	80	valid

Details

sample82.0ms

simplify95.0ms

prune2.0ms

localize11.0ms

rewrite43.0ms

series534.0ms

simplify88.0ms

prune324.0ms

localize12.0ms

rewrite52.0ms

series576.0ms

simplify82.0ms

prune294.0ms

localize11.0ms

rewrite50.0ms

series481.0ms

simplify82.0ms

prune234.0ms

localize12.0ms

rewrite54.0ms

series688.0ms

simplify112.0ms

prune282.0ms

regimes65.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling