Details

sample61.0ms

Algorithm

intervals

Results

15.0ms	194×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	100×	body	80	nan
7.0ms	28×	body	1280	valid
4.0ms	8×	body	320	valid
3.0ms	14×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
1.2b	(- (* b b) (* (* 4.0 a) c))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 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:

7.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 4.0 a) c)
43.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

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

prune282.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.2b	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
23.0b	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `distribute-lft-neg-in` `sqrt-prod`
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` `pow1/3` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt c)
3.0ms	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
5.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt c)
74.0ms	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
108.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
90.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	851
1	1236	747
2	5001	690

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.2b	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
23.0b	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `distribute-lft-neg-in` `sqrt-prod`
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` `pow1/3` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt c)
3.0ms	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
5.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt c)
65.0ms	(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
96.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
87.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	320	1340
1	1350	1203
2	5002	1083

prune345.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
9.5b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`fma-def` `add-log-exp`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip--`
2×	`pow1/3` `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 → 71

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (- 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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
234.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	366	848
1	1529	765
2	5002	749

prune326.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.2b

regimes187.0ms

Accuracy

84.8% (3.4b remaining)

Error of 15.4b against oracle of 12.0b and baseline of 34.3b

bsearch158.0ms

Steps

Iters	Range		Point
10	7.948130497386624e-31	1.6081733637561173e-14	5.082297393178073e-29
9	-2.2154171522802282e+61	-2.0511250318755918e+53	-2.0697892322852844e+57

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	25
1	39	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

446.0ms	5937×	body	80	valid
293.0ms	1019×	body	2560	valid
212.0ms	879×	body	1280	valid
205.0ms	2907×	body	80	nan
86.0ms	438×	body	640	valid
42.0ms	116×	body	5120	valid
40.0ms	250×	body	320	valid
12.0ms	106×	body	160	valid