Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
6.0ms	172×	body	80	valid
6.0ms	32×	body	1280	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

simplify11.0ms

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: 35.6b

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)))

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:

14.0ms	(/ (+ (- 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)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune274.0ms

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: 6.1b

Counts

103 → 10

localize17.0ms

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)))

rewrite52.0ms

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:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (+ 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)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
141.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
172.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify149.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (111.0ms)

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

prune517.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	242	12	254

Merged error: 6.0b

Counts

254 → 12

localize15.0ms

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)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
191×	`times-frac`
165×	`*-un-lft-identity`
123×	`add-cube-cbrt`
99×	`add-exp-log`
85×	`associate-r`
63×	`add-cbrt-cube`
60×	`prod-diff`
51×	`div-exp`
43×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
29×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
21×	`distribute-lft-neg-in`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
10×	`fma-neg`
9×	`div-inv`
8×	`add-log-exp` `unswap-sqr`
7×	`pow1` `neg-mul-1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
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 → 295

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(/ 3.0 (* a c))
55.0ms	(* (/ 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)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms	(/ 3.0 (* a c))
142.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1500	5617
1	5002	4095

prune622.0ms

Filtered

307 candidates to 167 candidates (54.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	3	7	10
Picked	1	0	1
Done	1	0	1
Total	309	10	319

Merged error: 6.0b

Counts

319 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 3.0 (* a c))
3.6b	(/ (/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
8.5b	(/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

2557×	`times-frac`
1360×	`add-sqr-sqrt`
1359×	`*-un-lft-identity`
835×	`add-cube-cbrt`
262×	`distribute-lft-out--` `difference-of-squares`
217×	`associate-/l*`
151×	`div-inv`
134×	`sqrt-prod`
131×	`distribute-rgt-neg-in`
46×	`associate-/r/`
43×	`add-exp-log` `add-cbrt-cube`
25×	`cbrt-undiv` `div-exp`
11×	`associate-/r*`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
2×	`sqrt-div` `associate-/l/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1056

Calls

4 calls:

4.0ms	(/ 3.0 (* a c))
50.0ms	(/ (/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
19.0ms	(/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 3.0 (* a c))
149.0ms	(/ (/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
169.0ms	(/ (/ 3.0 (/ 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify251.0ms

Algorithm

egg-herbie

Counts

1068 → 1068

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	3022	23478
1	5001	22405

prune2.3s

Filtered

1068 candidates to 575 candidates (53.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1066	2	1068
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	1069	9	1078

Merged error: 6.0b

Counts

1078 → 9

regimes349.0ms

Accuracy

82.2% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 31.4b

bsearch83.0ms

Steps

Iters	Range		Point
4	2.7062129888597453e-95	4.861630376334293e-95	3.8681552371770574e-95
9	-1.5394173084517817e+70	-1.6289578644700005e+63	-5.139138581373948e+66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

231.0ms	1054×	body	2560	valid
215.0ms	5816×	body	80	valid
155.0ms	889×	body	1280	valid
97.0ms	2865×	body	80	nan
65.0ms	470×	body	640	valid
29.0ms	111×	body	5120	valid
24.0ms	235×	body	320	valid
9.0ms	125×	body	160	valid