Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	204×	body	80	valid
6.0ms	29×	body	2560	valid
4.0ms	24×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite56.0ms

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:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune265.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.5b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
0.8b	(- (* b b) (* 3.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 3.0 (* a c))
105.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
42.0ms	(- (* b b) (* 3.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	330	529
1	1217	478
2	5001	467

prune256.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
2.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.9b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite86.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
46.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
146.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
173.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune415.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.2b

regimes415.0ms

Accuracy

84.4% (4.5b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.9b

bsearch96.0ms

Steps

Iters	Range		Point
8	1.0581952271802821e-68	3.094434386839899e-66	1.2392895115955295e-66
8	-3.7610221637517924e+157	-1.1271380753219535e+153	-4.198238632002835e+153

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	1101×	body	2560	valid
208.0ms	5784×	body	80	valid
156.0ms	896×	body	1280	valid
100.0ms	2794×	body	80	nan
68.0ms	483×	body	640	valid
28.0ms	107×	body	5120	valid
26.0ms	232×	body	320	valid
8.0ms	118×	body	160	valid