Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	32×	body	2560	valid
7.0ms	179×	body	80	valid
6.0ms	36×	body	1280	valid
4.0ms	110×	body	80	nan
1.0ms	13×	body	320	valid
1.0ms	9×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify13.0ms

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: 36.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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:

5.0ms	(* (* 3.0 a) c)
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

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

prune260.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
1.2b	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
1.4b	(- (* b b) (pow (* 3.0 (* a c)) 1))
25.8b	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

rewrite31.0ms

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:

5.0ms	(* 3.0 (* a c))
13.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
5.0ms	(- (* b b) (pow (* 3.0 (* a c)) 1))
6.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

series213.0ms

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))
67.0ms	(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (49.0ms)

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

prune284.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (* b b) (* (* 3.0 a) c))
25.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
25.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
50.0ms	(- (* b b) (* (* 3.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune294.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 3.0 a) c))
13.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
25.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

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:

4.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(+ (- 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)))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
83.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

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

prune280.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 14.5b

regimes236.0ms

Accuracy

87.6% (2.7b remaining)

Error of 15.2b against oracle of 12.5b and baseline of 34.5b

bsearch104.0ms

Steps

Iters	Range		Point
6	5.26864762567053e-15	2.5813273968244688e-14	5.333414018045465e-15
10	-6.984667632760565e+162	-7.224268075923972e+146	-1.3587793572260194e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	40	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

234.0ms	1095×	body	2560	valid
218.0ms	5837×	body	80	valid
161.0ms	935×	body	1280	valid
100.0ms	2925×	body	80	nan
60.0ms	448×	body	640	valid
26.0ms	101×	body	5120	valid
24.0ms	235×	body	320	valid
9.0ms	102×	body	160	valid