Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	34×	body	2560	valid
8.0ms	209×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	79×	body	80	nan
3.0ms	18×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

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: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
23.5b	(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:

38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(+ (- 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))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	855
1	1658	750
2	5001	735

prune304.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite88.0ms

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:

3.0ms	(- (* b b) (* 4.0 (* a c)))
47.0ms	(/ (/ (+ 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))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify112.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (90.0ms)

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

prune456.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
14.1b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	597	3032
1	2832	1946
2	5002	1857

prune308.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
64×	`add-exp-log` `*-un-lft-identity`
61×	`prod-diff`
60×	`add-cube-cbrt`
40×	`div-exp`
34×	`sqrt-prod`
31×	`times-frac`
25×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv` `fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

19.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(- (- 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))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	846	3812
1	3886	2561
2	5001	2521

prune349.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes265.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.4b against oracle of 5.3b and baseline of 29.2b

bsearch151.0ms

Steps

Iters	Range	Point
8	1.9559514031553493e+101	2.0413668072230428e+104	2.8991655454585953e+102
5	-1.2455002957733086e-223	-3.7018814373508505e-224	-3.7602322353181793e-224
9	-2.3467190644739184e+107	-3.2019781887028674e+101	-1.7431685240570133e+102

Iters

Range

Point

1.9559514031553493e+101

2.0413668072230428e+104

2.8991655454585953e+102

-1.2455002957733086e-223

-3.7018814373508505e-224

-3.7602322353181793e-224

-2.3467190644739184e+107

-3.2019781887028674e+101

-1.7431685240570133e+102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

248.0ms	1070×	body	2560	valid
232.0ms	5839×	body	80	valid
166.0ms	884×	body	1280	valid
102.0ms	2849×	body	80	nan
71.0ms	496×	body	640	valid
31.0ms	102×	body	5120	valid
26.0ms	220×	body	320	valid
8.0ms	103×	body	160	valid