Details

sample106.0ms

Algorithm

intervals

Results

29.0ms	124×	body	320	valid
22.0ms	513×	pre	80	true
18.0ms	257×	body	80	nan
12.0ms	87×	body	160	valid
3.0ms	12×	body	640	valid
2.0ms	33×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
27.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

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:

5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
5.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune778.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
28.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify152.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (113.0ms)

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

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
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))
0.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
8.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
87.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	598	2143
1	3014	1804
2	5002	1754

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
91×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
15×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `sum-log` `flip--` `associate-/l/`

Counts

4 → 184

Calls

4 calls:

37.0ms	(/ (/ (* 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))))
7.0ms	(/ (* 4.0 (* a c)) a)

series73.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (* 4.0 (* a c)) a)

simplify114.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	839	2756
1	4541	2477
2	5001	2473

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	25	11

end0.0ms

sample3.0s

Algorithm

intervals

Results

770.0ms	3603×	body	320	valid
691.0ms	16160×	pre	80	true
564.0ms	8160×	body	80	nan
427.0ms	2989×	body	160	valid
149.0ms	497×	body	640	valid
65.0ms	911×	body	80	valid