Details

sample72.0ms

Algorithm

intervals

Results

16.0ms	146×	body	160	valid
14.0ms	501×	pre	80	true
11.0ms	245×	body	80	nan
6.0ms	42×	body	320	valid
3.0ms	68×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	16
1	88	16

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 41.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* 3.0 (* a c)))
0.2b	(* 3.0 (* a c))
0.3b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
37.4b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`pow1`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-l` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`frac-2neg` `div-sub` `associate-r` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
10.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

series55.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
27.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
16.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

simplify34.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5007	1209

prune133.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 0.3b

Counts

88 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.2b	(* 3.0 (* a c))
0.3b	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.4b	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`add-exp-log` `add-cbrt-cube`
21×	`associate-/l*`
14×	`pow1`
10×	`distribute-lft-out`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l` `pow-prod-down` `associate-/r/`
5×	`associate-/r*`
4×	`div-inv` `add-log-exp`
3×	`flip3-+` `div-sub` `distribute-frac-neg` `flip-+` `associate-/l/`
2×	`frac-2neg` `sub0-neg` `associate-r` `clear-num` `*-commutative`
1×	`flip3--` `flip--`

Counts

4 → 131

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
5.0ms	(* 3.0 (* a c))
9.0ms	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
12.0ms	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

series104.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
3.0ms	(* 3.0 (* a c))
55.0ms	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
42.0ms	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

simplify38.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5247	2768

prune245.0ms

Filtered

97 candidates to 143 candidates (-47.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 0b

Counts

150 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
0.1b	(- (* b b) (* 3.0 (* a c)))
0.1b	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.2b	(* 3.0 (* a c))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
5×	`distribute-lft-out`
4×	`associate-/r*`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `flip--` `div-inv`

Counts

4 → 75

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(- (* b b) (* 3.0 (* a c)))
7.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))

series73.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
47.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(* 3.0 (* a c))

simplify71.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	1193
1	4949	1193

prune134.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 0b

Counts

96 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* 3.0 (* a c)))
0.2b	(* 3.0 (* a c))
0.3b	(/ (/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) a)
0.3b	(/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

305×	`times-frac`
194×	`*-un-lft-identity`
122×	`add-sqr-sqrt` `add-cube-cbrt`
44×	`add-exp-log`
41×	`associate-/l*`
36×	`distribute-lft-out`
32×	`add-cbrt-cube`
27×	`div-inv`
24×	`div-exp`
14×	`cbrt-undiv`
10×	`associate-/r/`
9×	`pow1`
7×	`prod-exp` `associate-/r*`
6×	`add-log-exp`
5×	`flip3-+` `distribute-frac-neg` `cbrt-unprod` `flip-+`
4×	`1-exp`
3×	`associate-l` `pow-prod-down`
2×	`frac-2neg` `clear-num` `distribute-rgt-neg-out` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

4 → 252

Calls

4 calls:

3.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
17.0ms	(/ (/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) a)
11.0ms	(/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(* 3.0 (* a c))
42.0ms	(/ (/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) a)
52.0ms	(/ (/ (* a (neg c)) 1) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4978	6685
1	4978	6685

prune373.0ms

Filtered

172 candidates to 264 candidates (-53.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	264	8	272

Merged error: 0b

Counts

272 → 8

regimes196.0ms

Accuracy

0% (0.1b 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 (1.0ms)

Iter	Nodes	Cost
0	26	15
1	26	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

458.0ms	4837×	body	160	valid
443.0ms	16129×	pre	80	true
390.0ms	8129×	body	80	nan
194.0ms	1352×	body	320	valid
91.0ms	1811×	body	80	valid

Details

sample72.0ms

simplify3.0ms

prune8.0ms

localize10.0ms

rewrite27.0ms

series55.0ms

simplify34.0ms

prune133.0ms

localize15.0ms

rewrite34.0ms

series104.0ms

simplify38.0ms

prune245.0ms

localize11.0ms

rewrite22.0ms

series73.0ms

simplify71.0ms

prune134.0ms

localize14.0ms

rewrite246.0ms

series107.0ms

simplify101.0ms

prune373.0ms

regimes196.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

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