Details

sample78.0ms

Algorithm

intervals

Results

41.0ms	969×	body	80	nan
13.0ms	290×	body	80	valid

simplify94.0ms

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)))
0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
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` `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)))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
204.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
272.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
105.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify103.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1008	1422
1	4619	1341
2	5001	1341

prune355.0ms

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)))))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite46.0ms

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)))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
12.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
8.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 9.0 (- a (/ 1.0 3.0)))
143.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
258.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
111.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (20.0ms)

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

prune256.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 0.0b

Counts

119 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
127×	`add-sqr-sqrt`
102×	`sqrt-prod`
89×	`*-un-lft-identity`
59×	`add-cube-cbrt`
26×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `flip3-+` `sqrt-div` `associate-r` `flip-+`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

6.0ms	(sqrt (- a (/ 1.0 3.0)))
30.0ms	(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
35.0ms	(* (- 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))))

series731.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- a (/ 1.0 3.0)))
175.0ms	(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
172.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
319.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1142	2786
1	5001	2617

prune624.0ms

Filtered

202 candidates to 132 candidates (65.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	203	8	211

Merged error: 0.0b

Counts

211 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0))))))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
72×	`times-frac`
61×	`*-un-lft-identity`
49×	`add-exp-log`
47×	`sqrt-prod`
43×	`add-cube-cbrt`
36×	`associate-r`
29×	`add-cbrt-cube`
17×	`prod-exp`
16×	`div-exp` `associate-l` `difference-of-squares`
10×	`pow1`
9×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv` `distribute-lft-out--`
6×	`add-log-exp` `unswap-sqr`
5×	`frac-times` `flip3--` `flip--`
4×	`rec-exp` `flip3-+` `sqrt-div` `1-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-r/` `associate-l/` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `un-div-inv` `inv-pow`

Counts

4 → 180

Calls

4 calls:

3.0ms	(+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0))))))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))))
9.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
26.0ms	(* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0))))))
177.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))))
101.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
323.0ms	(* (/ (* 1.0 rand) (sqrt 9.0)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1167	2272
1	5001	2039

prune394.0ms

Filtered

192 candidates to 121 candidates (63.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Merged error: 0.0b

Counts

200 → 7

regimes123.0ms

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	22	12
1	22	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	27491×	body	80	nan
422.0ms	9185×	body	80	valid

Details

sample78.0ms

simplify94.0ms

prune2.0ms

localize10.0ms

rewrite47.0ms

series725.0ms

simplify103.0ms

prune355.0ms

localize10.0ms

rewrite46.0ms

series556.0ms

simplify91.0ms

prune256.0ms

localize15.0ms

rewrite94.0ms

series731.0ms

simplify71.0ms

prune624.0ms

localize13.0ms

rewrite56.0ms

series780.0ms

simplify56.0ms

prune394.0ms

regimes123.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling