Details

sample42.0ms

Algorithm

intervals

Results

7.0ms	29×	body	2560	valid
7.0ms	181×	body	80	valid
5.0ms	26×	body	1280	valid
4.0ms	105×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	10×	body	160	valid
1.0ms	5×	body	320	valid

simplify11.0ms

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: 34.3b

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))
0.4b	(- (* b b) (* (* 3.0 a) c))
2.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
67.0ms	(- (* b b) (* (* 3.0 a) c))
104.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune214.0ms

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: 6.4b

Counts

83 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
0.4b	(- (* b b) (* (* 3.0 a) c))
2.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

13.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
3.0ms	(- (* 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)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
44.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	610	1962
1	2353	1864
2	5002	1843

prune351.0ms

Filtered

149 candidates to 102 candidates (68.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	148	11	159

Merged error: 6.4b

Counts

159 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
0.4b	(- (* b b) (* (* 3.0 a) c))
2.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

12.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
50.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	388	782
1	1552	682
2	5002	670

prune177.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	86	12	98

Merged error: 6.3b

Counts

98 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
2.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
52.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	281	466
1	1133	431
2	5001	428

prune137.0ms

Filtered

72 candidates to 50 candidates (69.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	73	11	84

Merged error: 6.3b

Counts

84 → 11

regimes481.0ms

Accuracy

82.2% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 34.0b

bsearch111.0ms

Steps

Iters	Range		Point
10	9.690537272714817e-102	1.7794146904278537e-90	1.761458221173807e-90
8	-1.0818597257815559e+95	-2.772945999025709e+91	-9.612795529269333e+93

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

230.0ms	1078×	body	2560	valid
209.0ms	5828×	body	80	valid
153.0ms	880×	body	1280	valid
109.0ms	3042×	body	80	nan
59.0ms	446×	body	640	valid
28.0ms	111×	body	5120	valid
25.0ms	248×	body	320	valid
10.0ms	124×	body	160	valid