Details

sample50.0ms

Algorithm

intervals

Results

13.0ms	45×	body	2560	valid
10.0ms	196×	body	80	valid
5.0ms	23×	body	1280	valid
5.0ms	96×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	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	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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: 35.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune264.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 5.9b

Counts

103 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
5.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
138.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
202.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	674	2663
1	3462	2412
2	5001	2406

prune568.0ms

Filtered

170 candidates to 117 candidates (68.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	168	11	179

Merged error: 5.8b

Counts

179 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
5.0b	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
9.0b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
16×	`add-sqr-sqrt` `cbrt-unprod`
15×	`*-un-lft-identity`
8×	`times-frac` `1-exp` `associate-/l*`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `associate-/l/`
2×	`distribute-rgt-neg-in` `frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-*r/` `prod-diff`

Counts

4 → 111

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
27.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
24.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 4.0 a) c))
153.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
130.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	785	1632
1	4111	1282
2	5002	1264

prune238.0ms

Filtered

123 candidates to 73 candidates (59.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	123	11	134

Merged error: 5.8b

Counts

134 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

14.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
41.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	514	1011
1	2322	856
2	5001	843

prune235.0ms

Filtered

112 candidates to 85 candidates (75.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	113	10	123

Merged error: 5.8b

Counts

123 → 10

regimes212.0ms

Accuracy

82.2% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 32.6b

bsearch98.0ms

Steps

Iters	Range		Point
7	3.9327484849495463e-50	8.339071351920685e-49	4.393815400015945e-50
7	-1.337582615490612e+92	-9.459320394366776e+89	-2.864598576127613e+91

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	31	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

337.0ms	1122×	body	2560	valid
295.0ms	5737×	body	80	valid
223.0ms	912×	body	1280	valid
145.0ms	2829×	body	80	nan
100.0ms	499×	body	640	valid
41.0ms	98×	body	5120	valid
31.0ms	220×	body	320	valid
11.0ms	117×	body	160	valid

Details

sample50.0ms

simplify11.0ms

prune2.0ms

localize11.0ms

rewrite33.0ms

series285.0ms

simplify48.0ms

prune264.0ms

localize15.0ms

rewrite56.0ms

series483.0ms

simplify123.0ms

prune568.0ms

localize26.0ms

rewrite70.0ms

series415.0ms

simplify94.0ms

prune238.0ms

localize12.0ms

rewrite33.0ms

series287.0ms

simplify61.0ms

prune235.0ms

regimes212.0ms

bsearch98.0ms

simplify1.0ms

end0.0ms

sample1.4s

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