Details

sample55.0ms

Algorithm

intervals

Results

13.0ms	153×	body	160	valid
10.0ms	504×	pre	80	true
8.0ms	248×	body	80	nan
5.0ms	48×	body	320	valid
2.0ms	55×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 45.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
40.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

107×	`*-un-lft-identity`
103×	`add-sqr-sqrt`
60×	`times-frac`
42×	`associate-l`
39×	`add-cube-cbrt`
28×	`distribute-lft-out` `unswap-sqr`
24×	`associate-r`
15×	`difference-of-squares`
14×	`add-exp-log` `distribute-rgt-neg-in` `add-cbrt-cube`
12×	`associate-/r*`
11×	`*-commutative`
10×	`add-log-exp`
9×	`pow1`
6×	`distribute-lft-out--`
5×	`associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`swap-sqr` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `neg-log` `clear-num` `flip--` `div-inv`

Counts

4 → 173

Calls

4 calls:

25.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(* (* 3.0 a) c)
42.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
120.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
94.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	630	2006
1	2832	1901
2	5001	1891

prune268.0ms

Filtered

185 candidates to 112 candidates (39.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Merged error: 0.2b

Counts

186 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* 3.0 (* a c))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

1793×	`*-un-lft-identity`
1346×	`times-frac`
919×	`add-sqr-sqrt`
400×	`distribute-lft-out` `distribute-lft-out--`
393×	`add-cube-cbrt`
389×	`associate-l`
200×	`difference-of-squares`
189×	`associate-r`
100×	`distribute-rgt-neg-in` `sqrt-prod`
69×	`associate-/l*`
64×	`unswap-sqr`
60×	`*-commutative`
28×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
26×	`associate-/r*`
23×	`associate-/l/`
15×	`div-inv`
14×	`pow1` `flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
2×	`associate-+l-` `flip3-+` `flip-+`

Counts

4 → 907

Calls

4 calls:

8.0ms	(* (* 3.0 a) c)
90.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(* 3.0 (* a c))
116.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series381.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
189.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
26.0ms	(* 3.0 (* a c))
143.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify252.0ms

Algorithm

egg-herbie

Counts

919 → 919

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1734	23796
1	5002	22807

prune1.3s

Filtered

919 candidates to 300 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	912	7	919
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	916	8	924

Merged error: 0b

Counts

924 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

2475×	`*-un-lft-identity`
1710×	`times-frac`
1129×	`add-sqr-sqrt`
840×	`associate-l`
600×	`distribute-lft-out`
556×	`distribute-lft-out--`
463×	`add-cube-cbrt`
256×	`difference-of-squares`
222×	`associate-r`
128×	`distribute-rgt-neg-in` `sqrt-prod`
87×	`associate-/l*`
78×	`unswap-sqr`
74×	`*-commutative`
28×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
26×	`associate-/r*`
25×	`associate-/l/`
15×	`div-inv`
14×	`pow1` `flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
2×	`associate-+l-` `flip3-+` `flip-+`

Counts

4 → 1107

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
8.0ms	(* (* 3.0 a) c)
92.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
120.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series378.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
27.0ms	(* (* 3.0 a) c)
186.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
142.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify293.0ms

Algorithm

egg-herbie

Counts

1119 → 1119

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1658	28820
1	5001	27475

prune1.1s

Filtered

1119 candidates to 303 candidates (72.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1117	2	1119
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	1122	5	1127

Merged error: 0b

Counts

1127 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* 3.0 (* a c))
0.3b	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.4b	(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

2578×	`times-frac`
2539×	`*-un-lft-identity`
2374×	`add-sqr-sqrt`
1520×	`associate-r`
1399×	`sqrt-prod`
1139×	`associate-l`
845×	`add-cube-cbrt`
522×	`distribute-lft-out--`
473×	`unswap-sqr`
432×	`distribute-lft-out`
306×	`difference-of-squares`
163×	`*-commutative`
153×	`distribute-rgt-neg-in`
150×	`associate-/l*`
44×	`associate-*r/`
37×	`add-exp-log` `add-cbrt-cube`
33×	`associate-/r*`
30×	`associate-/r/` `associate-/l/`
16×	`div-inv`
15×	`flip3--` `flip--`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
6×	`sqrt-div` `clear-num`
4×	`frac-2neg` `pow-prod-down` `un-div-inv` `add-log-exp`
3×	`flip3-+` `flip-+`

Counts

4 → 1876

Calls

4 calls:

91.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(* 3.0 (* a c))
140.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
187.0ms	(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

series1.3s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0ms	(* 3.0 (* a c))
489.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
463.0ms	(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

simplify596.0ms

Algorithm

egg-herbie

Counts

1888 → 1888

Iterations

Useful iterations: 1 (88.0ms)

Iter	Nodes	Cost
0	4626	60148
1	5001	59947

prune4.1s

Filtered

1888 candidates to 780 candidates (58.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1888	0	1888
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1888	5	1893

Merged error: 0b

Counts

1893 → 5

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

335.0ms	4814×	body	160	valid
305.0ms	16210×	pre	80	true
280.0ms	8210×	body	80	nan
148.0ms	1409×	body	320	valid
65.0ms	1777×	body	80	valid