Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	201×	body	80	valid
5.0ms	31×	body	1280	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

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize13.0ms

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)))

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-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))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
78.0ms	(+ (- 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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

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

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.9b

localize16.0ms

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

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
16.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
4.0ms	(- (* b b) (pow (* 3.0 (* a c)) 1))
7.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
75.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
42.0ms	(- (* b b) (pow (* 3.0 (* a c)) 1))
68.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

simplify63.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	395	716
1	1664	591
2	5001	580

prune269.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.9b

localize13.0ms

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)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

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)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	279	732
1	1153	610
2	5001	597

prune321.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.9b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
8×	`add-log-exp`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 72

Calls

4 calls:

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

series351.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (- b) (* (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	351	1045
1	1300	935
2	5001	925

prune397.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.9b

regimes302.0ms

Accuracy

80.8% (4.1b remaining)

Error of 16.8b against oracle of 12.7b and baseline of 34.1b

bsearch60.0ms

Steps

Iters	Range		Point
4	2.3785453177033023e+38	3.3068646783697877e+38	2.4075552977241297e+38
4	-2.4628825350256635e+163	-1.5405955983178716e+163	-1.5694170650899903e+163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

223.0ms	1100×	body	2560	valid
205.0ms	5848×	body	80	valid
158.0ms	920×	body	1280	valid
95.0ms	2886×	body	80	nan
63.0ms	452×	body	640	valid
28.0ms	103×	body	5120	valid
24.0ms	228×	body	320	valid
8.0ms	122×	body	160	valid