Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	189×	body	80	valid
10.0ms	34×	body	1280	valid
9.0ms	28×	body	2560	valid
5.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
3.0ms	7×	body	5120	valid
1.0ms	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

localize15.0ms

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)))

rewrite60.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune525.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

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)))

rewrite71.0ms

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:

42.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	646	2036
1	2495	1928
2	5001	1904

prune443.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
48×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
8×	`distribute-rgt-neg-in`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 134

Calls

4 calls:

28.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	556	1665
1	2707	1442
2	5001	1371

prune337.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

333×	`times-frac`
224×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out`
31×	`div-inv`
28×	`distribute-rgt-neg-in`
25×	`add-cbrt-cube`
21×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`fma-def` `add-log-exp`
9×	`flip3-+` `flip-+`
7×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 283

Calls

4 calls:

36.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1142	4787
1	5001	4210

prune510.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

regimes232.0ms

Accuracy

85.2% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch104.0ms

Steps

Iters	Range		Point
7	1.9426594712364374e-87	2.1051237392284573e-85	1.667046824505827e-85
8	-3.734333779790662e+128	-2.2987999557012895e+125	-5.238946631357967e+127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	1050×	body	2560	valid
237.0ms	5875×	body	80	valid
171.0ms	905×	body	1280	valid
105.0ms	2863×	body	80	nan
67.0ms	457×	body	640	valid
30.0ms	99×	body	5120	valid
23.0ms	212×	body	320	valid
9.0ms	128×	body	160	valid