Details

sample75.0ms

Algorithm

intervals

Results

17.0ms	283×	body	80	nan
15.0ms	153×	body	160	valid
15.0ms	539×	pre	80	true
5.0ms	103×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	16
1	91	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: 29.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
29.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

series65.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

simplify51.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4959	1319
1	4959	1319

prune133.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 0.4b

Counts

85 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
0.3b	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
9.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
60.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5103	3100

prune294.0ms

Filtered

98 candidates to 131 candidates (-33.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	4	0	4
Picked	1	0	1
Done	1	0	1
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))))) (* a 2.0))
0.3b	(* c (* 4.0 (* a c)))
0.3b	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b))))))
0.4b	(/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
58×	`*-un-lft-identity`
38×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/l*`
13×	`pow1`
10×	`distribute-lft-out`
8×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
6×	`pow-prod-down`
5×	`div-inv` `associate-/l/`
4×	`flip3-+` `div-sub` `flip-+` `add-log-exp`
3×	`frac-2neg` `distribute-frac-neg` `associate-l` `clear-num`
2×	`flip3--` `sub0-neg` `flip--`
1×	`associate-r` `*-commutative`

Counts

4 → 148

Calls

4 calls:

19.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))))) (* a 2.0))
7.0ms	(* c (* 4.0 (* a c)))
15.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b))))))
11.0ms	(/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))))) (* a 2.0))
4.0ms	(* c (* 4.0 (* a c)))
73.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b))))))
25.0ms	(/ (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (+ (* 4.0 (* a c)) (* b b)))

simplify80.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4924	5973
1	4924	5973

prune466.0ms

Filtered

119 candidates to 160 candidates (-34.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	161	12	173

Merged error: 0.0b

Counts

173 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (* 4.0 (* a c)) (* b b)))
0.3b	(* c (* 4.0 (* a c)))
0.3b	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b)))))))
0.4b	(* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
32×	`times-frac`
30×	`add-cube-cbrt`
28×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`pow1` `associate-r`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`pow-prod-down` `associate-/r*`
6×	`associate-l` `associate-/r/` `associate-/l*`
5×	`div-exp`
4×	`distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `flip3-+` `flip--` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-l/` `clear-num` `-commutative` `associate-/l/`
1×	`pow-flip` `sub0-neg` `div-sub` `associate-*r/` `distribute-frac-neg` `un-div-inv` `inv-pow`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/ 1 (+ (* 4.0 (* a c)) (* b b)))
9.0ms	(* c (* 4.0 (* a c)))
7.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b)))))))
14.0ms	(* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (+ (* 4.0 (* a c)) (* b b)))
4.0ms	(* c (* 4.0 (* a c)))
76.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b)))))))
22.0ms	(* (- (pow b 4) (* 4.0 (* a (* c (* 4.0 (* a c)))))) (/ 1 (+ (* 4.0 (* a c)) (* b b))))

simplify62.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4983	3628
1	4983	3628

prune306.0ms

Filtered

100 candidates to 145 candidates (-45.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	145	12	157

Merged error: 0.0b

Counts

157 → 12

regimes273.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	41
1	51	41

end0.0ms

sample2.2s

Algorithm

intervals

Results

564.0ms	4493×	body	160	valid
453.0ms	16674×	pre	80	true
412.0ms	8674×	body	80	nan
175.0ms	3507×	body	80	valid

Details

sample75.0ms

simplify3.0ms

prune8.0ms

localize10.0ms

rewrite28.0ms

series65.0ms

simplify51.0ms

prune133.0ms

localize13.0ms

rewrite33.0ms

series130.0ms

simplify41.0ms

prune294.0ms

localize23.0ms

rewrite56.0ms

series161.0ms

simplify80.0ms

prune466.0ms

localize23.0ms

rewrite41.0ms

series115.0ms

simplify62.0ms

prune306.0ms

regimes273.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

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