Details

sample67.0ms

Algorithm

intervals

Results

16.0ms	47×	body	2560	valid
11.0ms	167×	body	80	valid
9.0ms	32×	body	1280	valid
7.0ms	107×	body	80	nan
6.0ms	16×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify12.0ms

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: 35.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.2b	(- (* b b) (* (* 3.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:

7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (41.0ms)

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

prune255.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.5b	(fma b b (- (* (* 3.0 a) c)))
1.6b	(+ (- b) (sqrt (fma b b (- (* (* 3.0 a) c)))))
22.7b	(sqrt (fma b b (- (* (* 3.0 a) c))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
8×	`add-log-exp`
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×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `neg-log` `*-commutative` `flip-+` `fma-udef`

Counts

4 → 72

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
0.0ms	(fma b b (- (* (* 3.0 a) c)))
9.0ms	(+ (- b) (sqrt (fma b b (- (* (* 3.0 a) c)))))
1.0ms	(sqrt (fma b b (- (* (* 3.0 a) c))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
54.0ms	(fma b b (- (* (* 3.0 a) c)))
92.0ms	(+ (- b) (sqrt (fma b b (- (* (* 3.0 a) c)))))
85.0ms	(sqrt (fma b b (- (* (* 3.0 a) c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	276	448
1	1054	395
2	5001	386

prune225.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	234	668
1	888	610
2	3709	588
3	5001	584

prune378.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize26.0ms

Local error

Found 4 expressions with local error:

10.4b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite18.0ms

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:

7.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	391	873
1	1592	796
2	5001	765

prune427.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

regimes248.0ms

Accuracy

87.6% (2.8b remaining)

Error of 15.1b against oracle of 12.3b and baseline of 34.8b

bsearch155.0ms

Steps

Iters	Range		Point
8	2.7436979961372665e-42	4.0592445250007856e-39	1.8843431932504646e-40
12	-7.927726045730789e+181	-4.544878892552954e+140	-1.3379185299605649e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	21
1	48	21
2	48	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

406.0ms	5746×	body	80	valid
385.0ms	1107×	body	2560	valid
265.0ms	929×	body	1280	valid
177.0ms	2804×	body	80	nan
111.0ms	479×	body	640	valid
44.0ms	106×	body	5120	valid
36.0ms	215×	body	320	valid
17.0ms	118×	body	160	valid