Details

sample81.0ms

Algorithm

intervals

Results

44.0ms	973×	body	80	nan
13.0ms	293×	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: 0.2b

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)))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite48.0ms

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)))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
12.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series756.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
282.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
212.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
109.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4617	1341
2	5001	1341

prune348.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

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)))))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.8b	(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)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
11.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 9.0 (- a (/ 1.0 3.0)))
148.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
272.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
108.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	870	1101
1	4263	1027
2	5001	1027

prune252.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Merged error: 0.0b

Counts

118 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(- a (/ 1.0 3.0))
0.1b	(* (- 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))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
130×	`add-sqr-sqrt`
96×	`sqrt-prod`
88×	`*-un-lft-identity`
58×	`add-cube-cbrt`
28×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`pow1` `flip3--` `associate-l` `flip--`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `associate-r`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

6.0ms	(- a (/ 1.0 3.0))
6.0ms	(- a (/ 1.0 3.0))
40.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
15.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- a (/ 1.0 3.0))
23.0ms	(- a (/ 1.0 3.0))
180.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
375.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify121.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1050	2579
1	4918	2422
2	5001	2422

prune443.0ms

Filtered

202 candidates to 128 candidates (63.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	203	7	210

Merged error: 0.0b

Counts

210 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
0.8b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
6.6b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite57.0ms

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:

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)))))
7.0ms	(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))

series866.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
215.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
114.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
248.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify92.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	973	1339
1	4224	1216
2	5001	1216

prune303.0ms

Filtered

123 candidates to 99 candidates (80.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	125	5	130

Merged error: 0.0b

Counts

130 → 5

regimes63.0ms

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

sample2.1s

Algorithm

intervals

Results

1.2s	28031×	body	80	nan
408.0ms	9189×	body	80	valid

Details

sample81.0ms

simplify95.0ms

prune2.0ms

localize10.0ms

rewrite48.0ms

series756.0ms

simplify105.0ms

prune348.0ms

localize10.0ms

rewrite48.0ms

series574.0ms

simplify92.0ms

prune252.0ms

localize11.0ms

rewrite76.0ms

series607.0ms

simplify121.0ms

prune443.0ms

localize11.0ms

rewrite57.0ms

series866.0ms

simplify92.0ms

prune303.0ms

regimes63.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.1s

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