Details

sample122.0ms

Algorithm

intervals

Results

29.0ms	185×	body	80	valid
21.0ms	30×	body	2560	valid
17.0ms	25×	body	1280	valid
14.0ms	99×	body	80	nan
10.0ms	20×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite101.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
5.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

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

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.2b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.9b	(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))
45.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 3.0 a) c))
140.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
174.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify121.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (99.0ms)

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

prune436.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.2b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
18.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
150.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
177.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	714	2019
1	4679	1554
2	5001	1549

prune345.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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)
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

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

prune219.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes345.0ms

Accuracy

86.1% (3.7b remaining)

Error of 9.3b against oracle of 5.6b and baseline of 32.5b

bsearch186.0ms

Steps

Iters	Range	Point
7	6.714891876596302e+121	1.686395921989292e+123	7.240249926714303e+121
6	7.361484502541699e-117	4.0357577402084977e-116	7.481934651249181e-117
8	-2.1136969993533704e+133	-9.628024177185589e+129	-2.1419401754731713e+130

Iters

Range

Point

6.714891876596302e+121

1.686395921989292e+123

7.240249926714303e+121

7.361484502541699e-117

4.0357577402084977e-116

7.481934651249181e-117

-2.1136969993533704e+133

-9.628024177185589e+129

-2.1419401754731713e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	49	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

538.0ms	5893×	body	80	valid
451.0ms	1083×	body	2560	valid
306.0ms	895×	body	1280	valid
254.0ms	2933×	body	80	nan
121.0ms	440×	body	640	valid
61.0ms	117×	body	5120	valid
53.0ms	227×	body	320	valid
15.0ms	98×	body	160	valid