Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	30×	body	2560	valid
0.0hr	200×	body	80	valid
0.0hr	31×	body	1280	valid
0.0hr	85×	body	80	nan
0.0hr	15×	body	640	valid
0.0hr	4×	body	5120	valid
0.0hr	4×	body	320	valid
0.0hr	2×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune0.0hr

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.6b

Counts

2 → 1

localize0.0hr

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

0.0hr	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.0hr	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.0hr	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

simplify0.0hr

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune0.0hr

Filtered

92 candidates to 69 candidates (25.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	7	93

Merged error: 5.1b

Counts

93 → 7

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

0.0hr	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.0hr	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.0hr	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

simplify0.0hr

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	428	816
1	1923	721
2	5001	680

prune0.0hr

Filtered

96 candidates to 71 candidates (26.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 5.1b

Counts

103 → 7

localize0.0hr

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.1b	(* (/ 1 a) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(* (/ 1 a) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(* (/ 1 a) (* a c))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

simplify0.0hr

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	403	531
1	1916	427
2	5001	419

prune0.0hr

Filtered

94 candidates to 63 candidates (33.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	94	7	101

Merged error: 5.0b

Counts

101 → 7

localize0.0hr

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0hr	(/ (+ (* (/ 1 a) 0) c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (+ (* (/ 1 a) 0) c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.0hr	(- (* b_2 b_2) (* a c))
0.0hr	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.0hr	(sqrt (- (* b_2 b_2) (* a c)))

simplify0.0hr

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	389	1170
1	1550	1051
2	5002	1034

prune0.0hr

Filtered

104 candidates to 74 candidates (28.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	104	7	111

Merged error: 5.0b

Counts

111 → 7

regimes0.0hr

Accuracy

96.1% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.2b

bsearch0.0hr

Steps

Iters	Range	Point
9	3.763859088204499e+91	2.271321644956683e+99	1.704059040904738e+99
8	-2.450180232760445e-303	-6.101116520471646e-307	-3.035384695936534e-304
9	-3.6502939682616286e+159	-2.0984588557191883e+153	-2.336606735933724e+153

Iters

Range

Point

3.763859088204499e+91

2.271321644956683e+99

1.704059040904738e+99

-2.450180232760445e-303

-6.101116520471646e-307

-3.035384695936534e-304

-3.6502939682616286e+159

-2.0984588557191883e+153

-2.336606735933724e+153

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	43	24
1	43	24

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	1043×	body	2560	valid
0.0hr	5858×	body	80	valid
0.0hr	924×	body	1280	valid
0.0hr	2794×	body	80	nan
0.0hr	483×	body	640	valid
0.0hr	113×	body	5120	valid
0.0hr	237×	body	320	valid
0.0hr	99×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

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