Details

sample52.0ms

Algorithm

intervals

Results

13.0ms	521×	pre	80	true
9.0ms	265×	body	80	nan
9.0ms	128×	body	160	valid
4.0ms	128×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
25.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune265.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- 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)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828

prune565.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `fma-udef`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
227.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
167.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
267.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	598	2144
1	3014	1804
2	5002	1754

prune430.0ms

Filtered

117 candidates to 96 candidates (82.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
90×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
14×	`div-inv`
12×	`associate-/r*`
8×	`neg-mul-1` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
35.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
151.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify117.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	841	2767
1	4480	2589
2	5003	2585

prune486.0ms

Filtered

188 candidates to 133 candidates (70.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	31	13
2	31	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

305.0ms	4404×	body	160	valid
294.0ms	16698×	pre	80	true
279.0ms	8698×	body	80	nan
123.0ms	3596×	body	80	valid