Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
8.0ms	198×	body	80	valid
6.0ms	92×	body	80	nan
4.0ms	24×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	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: 34.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
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 → 70

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune236.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

54.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	479	920
1	2139	790
2	5002	777

prune245.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
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 → 70

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune205.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

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` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
48.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	145	476
1	528	446
2	2232	444
3	5002	440

prune230.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.8b

regimes263.0ms

Accuracy

84.9% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 34.5b

bsearch119.0ms

Steps

Iters	Range		Point
9	3.6106127752583374e-71	6.7695755698382385e-65	9.390367471089922e-69
9	-8.652530131639494e+154	-2.4576771469086066e+149	-2.9358923729233266e+149

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

272.0ms	1117×	body	2560	valid
234.0ms	5730×	body	80	valid
183.0ms	928×	body	1280	valid
111.0ms	2856×	body	80	nan
73.0ms	473×	body	640	valid
29.0ms	100×	body	5120	valid
28.0ms	244×	body	320	valid
8.0ms	108×	body	160	valid