Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
7.0ms	183×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	90×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	320	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.6b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 73

Calls

4 calls:

16.0ms	(* (* 4.0 a) c)
66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* 4.0 a) c)
95.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	430	682
1	1845	594
2	5001	588

prune224.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
0.6b	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

27.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
86.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
9.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
12.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
97.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
39.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
64.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	411	904
1	1550	792
2	5002	780

prune245.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `sqrt-prod` `associate-/l*`
4×	`difference-of-squares`
3×	`associate-/r*`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

29.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
82.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
9.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
12.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
92.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) a)
40.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
66.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify45.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	375	1043
1	1383	957
2	5001	940

prune289.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
0.3b	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
137×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
32×	`distribute-lft-out`
26×	`associate-/r*`
17×	`add-exp-log`
16×	`distribute-rgt-neg-in`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `difference-of-squares`
2×	`rec-exp` `flip3--` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `flip--` `sqr-pow`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `inv-pow`

Counts

4 → 176

Calls

4 calls:

60.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
54.0ms	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
9.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
12.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))))
181.0ms	(/ a (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))))
39.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
66.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify74.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	566	2727
1	2634	2426
2	5001	2304

prune375.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

regimes293.0ms

Accuracy

84.3% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.7b

bsearch97.0ms

Steps

Iters	Range		Point
10	2.2777662256792016e-86	1.8614563384609176e-67	6.172683485094139e-78
4	-1.5284190780878897e+101	-8.96616642260002e+100	-1.3754558446128672e+101

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	41	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1127×	body	2560	valid
230.0ms	5786×	body	80	valid
164.0ms	916×	body	1280	valid
103.0ms	2998×	body	80	nan
66.0ms	438×	body	640	valid
29.0ms	105×	body	5120	valid
23.0ms	222×	body	320	valid
8.0ms	117×	body	160	valid