Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	31×	body	1280	valid
7.0ms	201×	body	80	valid
4.0ms	21×	body	2560	valid
3.0ms	103×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
19.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`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-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
11.0ms	(+ (- 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)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune190.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
1.0b	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
1.2b	(- (* b b) (pow (* 3.0 (* a c)) 1))
19.5b	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
6×	`add-cube-cbrt`
5×	`sqrt-prod`
4×	`difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `*-commutative` `flip-+`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
18.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
3.0ms	(- (* b b) (pow (* 3.0 (* a c)) 1))
6.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
79.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
47.0ms	(- (* b b) (pow (* 3.0 (* a c)) 1))
68.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	316	556
1	1196	502
2	5002	494

prune211.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
11.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
19.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))
19.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 55

Calls

4 calls:

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	251	648
1	1020	537
2	4512	523
3	5002	521

prune243.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.6b

localize26.0ms

Local error

Found 4 expressions with local error:

11.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
19.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.3b	(cbrt (- (* b b) (* (* 3.0 a) c)))
20.3b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

Calls

4 calls:

5.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	330	962
1	1206	852
2	4939	841
3	5001	841

prune322.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.6b

regimes410.0ms

Accuracy

95.5% (1.0b remaining)

Error of 13.5b against oracle of 12.5b and baseline of 34.1b

bsearch164.0ms

Steps

Iters	Range	Point
7	1.4883044572870273e+152	8.269463047302798e+153	4.898816022123459e+152
11	1.1414292389183633e-196	1.3084218714024342e-176	1.1928781235179368e-176
4	-2.4628825350256635e+163	-1.5405955983178716e+163	-1.5694170650899903e+163

Iters

Range

Point

1.4883044572870273e+152

8.269463047302798e+153

4.898816022123459e+152

1.1414292389183633e-196

1.3084218714024342e-176

1.1928781235179368e-176

-2.4628825350256635e+163

-1.5405955983178716e+163

-1.5694170650899903e+163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	34
1	54	34
2	54	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

241.0ms	1100×	body	2560	valid
209.0ms	5848×	body	80	valid
156.0ms	920×	body	1280	valid
96.0ms	2886×	body	80	nan
59.0ms	452×	body	640	valid
28.0ms	103×	body	5120	valid
23.0ms	228×	body	320	valid
8.0ms	122×	body	160	valid