Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
6.0ms	29×	body	2560	valid
4.0ms	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
0.0ms	5×	body	320	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: 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)))

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)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune255.0ms

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: 6.4b

Counts

103 → 10

localize14.0ms

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)))

rewrite35.0ms

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:

13.0ms	(/ (/ (+ (- 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)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
42.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

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

prune351.0ms

Filtered

169 candidates to 121 candidates (71.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	169	10	179

Merged error: 6.4b

Counts

179 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 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)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`times-frac`
26×	`add-exp-log`
24×	`add-cube-cbrt`
19×	`associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
10×	`fma-def` `add-log-exp`
8×	`div-exp` `prod-exp` `distribute-lft-out`
7×	`pow1` `distribute-rgt-neg-in`
6×	`unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 124

Calls

4 calls:

19.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 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)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	645	1311
1	3129	1145
2	5001	1130

prune290.0ms

Filtered

136 candidates to 98 candidates (72.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	136	10	146

Merged error: 6.4b

Counts

146 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.8b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.9b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

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

series503.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
172.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
179.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify149.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (110.0ms)

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

prune474.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	240	4	244
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	240	14	254

Merged error: 6.3b

Counts

254 → 14

regimes774.0ms

Accuracy

82.3% (5.0b remaining)

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

bsearch114.0ms

Steps

Iters	Range		Point
10	9.690537272714817e-102	1.7794146904278537e-90	1.761458221173807e-90
8	-1.0818597257815559e+95	-2.772945999025709e+91	-8.176952505904844e+94

simplify2.0ms

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

238.0ms	1078×	body	2560	valid
220.0ms	5828×	body	80	valid
154.0ms	880×	body	1280	valid
103.0ms	3042×	body	80	nan
67.0ms	446×	body	640	valid
33.0ms	111×	body	5120	valid
26.0ms	248×	body	320	valid
11.0ms	124×	body	160	valid