Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	32×	body	1280	valid
7.0ms	34×	body	2560	valid
6.0ms	172×	body	80	valid
3.0ms	79×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 35.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
49.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune224.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.1b

Counts

83 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.6b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.8b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

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

series485.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
187.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune436.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	165	11	176

Merged error: 6.0b

Counts

176 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(/ 3.0 (* a c))
16.2b	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
151×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
99×	`add-exp-log`
85×	`associate-r`
82×	`add-cube-cbrt`
63×	`add-cbrt-cube`
51×	`div-exp`
29×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
9×	`div-inv`
8×	`add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`associate-/l*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `-commutative`

Counts

4 → 217

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(/ 3.0 (* a c))
59.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0ms	(/ 3.0 (* a c))
153.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1326	3208
1	5002	2637

prune594.0ms

Filtered

229 candidates to 142 candidates (62.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	230	10	240

Merged error: 6.0b

Counts

240 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune168.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	71	11	82

Merged error: 6.0b

Counts

82 → 11

regimes367.0ms

Accuracy

83.4% (4.5b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 32.2b

bsearch77.0ms

Steps

Iters	Range		Point
4	2.7062129888597453e-95	4.861630376334293e-95	3.8681552371770574e-95
9	-1.8864815038392082e+94	-1.5243980513895428e+89	-6.875360452843506e+92

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

248.0ms	1054×	body	2560	valid
237.0ms	5816×	body	80	valid
169.0ms	889×	body	1280	valid
106.0ms	2865×	body	80	nan
75.0ms	470×	body	640	valid
36.0ms	111×	body	5120	valid
26.0ms	235×	body	320	valid
9.0ms	125×	body	160	valid