Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify113.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	665	2663
1	3259	2412
2	5001	2405

prune423.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
3.7b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
8.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `distribute-rgt-neg-in` `associate-r` `associate-/r*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 153

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
147.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
183.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify137.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	758	2388
1	4031	2057
2	5001	2054

prune396.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
15.1b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 152

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify134.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	663	3384
1	3444	2233
2	5001	2228

prune341.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes196.0ms

Accuracy

83.8% (4.3b remaining)

Error of 9.6b against oracle of 5.3b and baseline of 31.8b

bsearch130.0ms

Steps

Iters	Range		Point
9	3.2956103981062554e-86	3.6842556330088986e-79	2.267195199467958e-82
11	-1.7053146236540368e+120	-1.0719231849388273e+91	-3.5940112039867074e+100

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

248.0ms	1080×	body	2560	valid
232.0ms	5783×	body	80	valid
173.0ms	928×	body	1280	valid
113.0ms	2980×	body	80	nan
67.0ms	450×	body	640	valid
29.0ms	105×	body	5120	valid
28.0ms	258×	body	320	valid
9.0ms	123×	body	160	valid