Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
6.0ms	34×	body	1280	valid
6.0ms	28×	body	2560	valid
4.0ms	7×	body	5120	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune307.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

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:

4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (100.0ms)

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

prune484.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
16.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 150

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune341.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
64×	`add-exp-log` `*-un-lft-identity`
61×	`prod-diff`
60×	`add-cube-cbrt`
40×	`div-exp`
34×	`sqrt-prod`
31×	`times-frac`
25×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv` `fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

16.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	845	3812
1	3929	2561
2	5001	2521

prune357.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

regimes195.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.7b

bsearch171.0ms

Steps

Iters	Range		Point
5	1.1874868645648804e+84	3.824179182553312e+84	3.771181145902542e+84
9	6.841012161467506e-264	8.954106309325026e-259	7.170478586447025e-264
8	-3.734333779790662e+128	-2.2987999557012895e+125	-5.238946631357967e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	1050×	body	2560	valid
235.0ms	5875×	body	80	valid
170.0ms	905×	body	1280	valid
110.0ms	2863×	body	80	nan
67.0ms	457×	body	640	valid
28.0ms	99×	body	5120	valid
23.0ms	212×	body	320	valid
9.0ms	128×	body	160	valid