Details

sample43.0ms

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
2.0ms	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

localize14.0ms

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)))

rewrite100.0ms

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)
65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series213.0ms

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))
38.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (44.0ms)

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

prune223.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize13.0ms

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))))
84.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
11.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
12.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
93.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) (* 2.0 a))
41.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
63.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (39.0ms)

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

prune236.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) 2.0)
0.6b	(- (* b b) (pow (* 4.0 (* a c)) 1))
26.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite132.0ms

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:

27.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
82.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) 2.0)
9.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
12.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))))
80.0ms	(/ (+ (- b) (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))) 2.0)
39.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
65.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify45.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	355	1039
1	1296	956
2	5002	935

prune266.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

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-/r*`
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` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

16.0ms	(* (* 4.0 a) c)
45.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 4.0 a) c)
174.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
39.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	394	655
1	1796	565
2	5001	558

prune180.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

regimes321.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 34.4b

bsearch108.0ms

Steps

Iters	Range		Point
10	2.2777662256792016e-86	1.8614563384609176e-67	1.2091207453430995e-70
6	-1.3854637168610187e+102	-1.5284190780878897e+101	-9.912439588753869e+101

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

247.0ms	1127×	body	2560	valid
225.0ms	5786×	body	80	valid
164.0ms	916×	body	1280	valid
109.0ms	2998×	body	80	nan
63.0ms	438×	body	640	valid
28.0ms	105×	body	5120	valid
24.0ms	222×	body	320	valid
8.0ms	117×	body	160	valid