Details

sample610.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 99.999783%

Space saved by search: 99.99989%

Guaranteed chance to sample good point: 87.710337%

Results

13.0ms	142×	body	160	valid
8.0ms	277×	pre	80	true
6.0ms	114×	body	80	valid
3.0ms	21×	body	80	nan

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

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: 30.0b

Counts

2 → 1

localize12.0ms

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	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.9b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
19.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune133.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.4b

Counts

83 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	643	2666
1	3210	2408
2	5001	2396

prune316.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	152	11	163
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	157	11	168

Merged error: 0.0b

Counts

168 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log`
71×	`add-cbrt-cube`
64×	`prod-exp`
40×	`div-exp`
32×	`cbrt-unprod`
20×	`cbrt-undiv`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`pow1`
8×	`add-cube-cbrt` `rec-exp` `1-exp`
7×	`associate-r`
6×	`flip3--` `flip--`
5×	`associate-l` `associate-/r/`
4×	`frac-times` `sub-neg` `times-frac` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-/l*`
2×	`distribute-rgt-in` `pow-flip` `distribute-rgt-neg-in` `distribute-lft-in` `pow-prod-down` `associate-*l/` `sqrt-prod` `div-inv`
1×	`associate--l-` `neg-sub0` `frac-2neg` `neg-log` `clear-num` `associate-/r` `-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	843	2156
1	5001	1664

prune186.0ms

Filtered

73 candidates to 144 candidates (-97.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	146	9	155

Merged error: 0b

Counts

155 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ 1 (* (/ 2.0 4.0) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
38×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`times-frac` `add-cbrt-cube`
23×	`div-exp`
18×	`add-cube-cbrt`
12×	`prod-exp`
10×	`cbrt-undiv` `associate-/l*` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1`
5×	`rec-exp` `distribute-rgt-neg-in` `1-exp` `sqrt-prod`
4×	`associate-/r*` `cbrt-unprod`
3×	`flip3--` `diff-log` `associate-/r/` `flip--`
2×	`sub-neg` `pow-flip` `frac-2neg` `clear-num` `div-inv` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `div-sub` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `inv-pow`

Counts

4 → 119

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)
4.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ 1 (* (/ 2.0 4.0) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)
8.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(/ 1 (* (/ 2.0 4.0) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	642	1587
1	2784	1393
2	5003	1387

prune151.0ms

Filtered

76 candidates to 131 candidates (-72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Merged error: 0b

Counts

140 → 9

regimes215.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 99.999783%

Space saved by search: 99.99989%

Guaranteed chance to sample good point: 87.710337%

Results

431.0ms	4449×	body	160	valid
248.0ms	8437×	pre	80	true
178.0ms	3550×	body	80	valid
21.0ms	437×	body	80	nan
0.0ms	1×	body	320	valid

Details

sample610.0ms

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite28.0ms

series68.0ms

simplify46.0ms

prune133.0ms

localize16.0ms

rewrite49.0ms

series125.0ms

simplify115.0ms

prune316.0ms

localize19.0ms

rewrite51.0ms

series94.0ms

simplify41.0ms

prune186.0ms

localize14.0ms

rewrite43.0ms

series76.0ms

simplify68.0ms

prune151.0ms

regimes215.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

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