Details

sample37.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
6.0ms	180×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	75×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	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: 35.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune247.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	10	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 5.9b

Counts

103 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

13.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
142.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
175.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify146.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune447.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	244	10	254

Merged error: 5.8b

Counts

254 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.5b	(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
8.7b	(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
48×	`add-exp-log`
37×	`sqrt-prod`
30×	`add-cbrt-cube`
27×	`associate-r`
25×	`distribute-rgt-neg-in`
24×	`times-frac`
21×	`distribute-lft-neg-in`
17×	`prod-exp`
16×	`div-exp`
10×	`fma-neg`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `neg-mul-1`
6×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `associate-l` `flip--` `unswap-sqr`
2×	`sqrt-div` `diff-log` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 200

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms	(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
20.0ms	(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
151.0ms	(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
174.0ms	(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	910	4210
1	5002	2933

prune401.0ms

Filtered

212 candidates to 112 candidates (52.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	212	10	222

Merged error: 5.8b

Counts

222 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
116×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/l*`
16×	`distribute-rgt-neg-in`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-neg-in` `div-exp` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `sqrt-div` `div-sub` `sum-log` `flip--`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

17.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
4.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
45.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	643	2037
1	2492	1929
2	5001	1905

prune322.0ms

Filtered

169 candidates to 121 candidates (71.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	168	11	179

Merged error: 5.8b

Counts

179 → 11

regimes425.0ms

Accuracy

80.5% (5.3b remaining)

Error of 10.7b against oracle of 5.4b and baseline of 32.7b

bsearch115.0ms

Steps

Iters	Range		Point
9	7.30455191105786e-90	1.8075577067303308e-84	1.4297233981116778e-84
7	-2.501148282372368e+59	-1.593441833549377e+57	-2.21751057489785e+59

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

225.0ms	1050×	body	2560	valid
218.0ms	5823×	body	80	valid
161.0ms	883×	body	1280	valid
96.0ms	2908×	body	80	nan
66.0ms	488×	body	640	valid
25.0ms	243×	body	320	valid
24.0ms	91×	body	5120	valid
9.0ms	132×	body	160	valid