Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	186×	body	80	valid
5.0ms	25×	body	1280	valid
5.0ms	8×	body	5120	valid
3.0ms	82×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	6×	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: 33.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

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:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(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	405	779
1	1563	685
2	5001	674

prune215.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
139.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
173.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
8.6b	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
20.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
174.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	643	1677
1	3301	1344
2	5003	1325

prune311.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.8b	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))))
16.3b	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

5.0ms	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))))
20.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))))
76.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	461	1095
1	2220	928
2	5002	902

prune288.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes203.0ms

Accuracy

74.3% (7.0b remaining)

Error of 12.4b against oracle of 5.4b and baseline of 32.6b

bsearch162.0ms

Steps

Iters	Range		Point
10	4.734590495924167e-35	7.237368999400794e-22	1.5846768506177574e-31
11	-1.1860998636736231e+119	-1.6133553378404837e+99	-1.6406413729723635e+109

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	25
1	46	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

267.0ms	1073×	body	2560	valid
245.0ms	5835×	body	80	valid
177.0ms	903×	body	1280	valid
115.0ms	2961×	body	80	nan
73.0ms	451×	body	640	valid
30.0ms	259×	body	320	valid
26.0ms	90×	body	5120	valid
9.0ms	118×	body	160	valid