Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	204×	body	80	valid
6.0ms	28×	body	2560	valid
6.0ms	91×	body	80	nan
4.0ms	25×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(+ (- 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))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune240.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

56.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms	(+ (- 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))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	479	920
1	2139	790
2	5002	777

prune233.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
2.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.8b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite85.0ms

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×	`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` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
147.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	628	2579
1	2954	2333
2	5001	2320

prune419.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.2b

localize18.0ms

Local error

Found 4 expressions with local error:

6.5b	(- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
10.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))))
21.5b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.5b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `cbrt-div` `flip3--` `flip--`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 71

Calls

4 calls:

6.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series899.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
607.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))))
98.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
101.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	622	1757
1	2850	1587
2	5001	1578

prune371.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.2b

regimes246.0ms

Accuracy

80.2% (5.3b remaining)

Error of 11.1b against oracle of 5.7b and baseline of 32.7b

bsearch180.0ms

Steps

Iters	Range	Point
10	2.5901373358104347e+70	6.108550930002793e+80	2.5462987357189736e+71
5	-3.798273980088639e-127	-1.2883737028483634e-127	-1.3119329296566595e-127
8	-6.6886088143369254e+38	-2.2615366197350152e+35	-5.531732578640944e+38

Iters

Range

Point

2.5901373358104347e+70

6.108550930002793e+80

2.5462987357189736e+71

-3.798273980088639e-127

-1.2883737028483634e-127

-1.3119329296566595e-127

-6.6886088143369254e+38

-2.2615366197350152e+35

-5.531732578640944e+38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	42
1	53	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

250.0ms	1099×	body	2560	valid
215.0ms	5785×	body	80	valid
162.0ms	897×	body	1280	valid
100.0ms	2794×	body	80	nan
75.0ms	483×	body	640	valid
29.0ms	108×	body	5120	valid
24.0ms	232×	body	320	valid
8.0ms	118×	body	160	valid