Details

sample73.0ms

Algorithm

intervals

Results

14.0ms	34×	body	1280	valid
12.0ms	189×	body	80	valid
11.0ms	28×	body	2560	valid
6.0ms	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

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize19.0ms

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)))

rewrite87.0ms

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:

49.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

46.0ms	(/ (+ (sqrt (- (* b b) (* (* 4.0 a) c))) (- b)) (* 2.0 a))
19.0ms	(+ (sqrt (- (* b b) (* (* 4.0 a) c))) (- b))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (sqrt (- (* b b) (* (* 4.0 a) c))) (- b)) (* 2.0 a))
77.0ms	(+ (sqrt (- (* b b) (* (* 4.0 a) c))) (- b))
59.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	439	865
1	1792	764
2	5002	756

prune247.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize12.0ms

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:

27.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (56.0ms)

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

prune312.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

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)))

rewrite80.0ms

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-l`
5×	`distribute-rgt-neg-in` `associate-r`
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-*r/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

57.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	540	1014
1	2856	861
2	5001	850

prune267.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

regimes220.0ms

Accuracy

85.4% (4.1b remaining)

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

bsearch93.0ms

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	33	15
1	33	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

237.0ms	1050×	body	2560	valid
229.0ms	5875×	body	80	valid
168.0ms	905×	body	1280	valid
107.0ms	2863×	body	80	nan
65.0ms	457×	body	640	valid
27.0ms	99×	body	5120	valid
23.0ms	212×	body	320	valid
9.0ms	128×	body	160	valid