Details

sample285.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	33×	body	1280	valid
6.0ms	181×	body	80	valid
3.0ms	92×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

11.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune320.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 284

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505

prune635.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
76×	`add-cube-cbrt`
60×	`prod-diff`
58×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
28×	`add-exp-log`
27×	`associate-l`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
10×	`fma-neg`
9×	`div-exp`
8×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-/r*`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 229

Calls

4 calls:

11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
16.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
178.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	889	4144
1	3959	3028
2	5001	3027

prune505.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.1b	(/ (* a c) a)
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `times-frac` `diff-log` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 146

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (* a c) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	480	2539
1	1838	1650
2	5002	1553

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes187.0ms

Accuracy

87.8% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.5b

bsearch77.0ms

Steps

Iters	Range	Point
3	5.062782482725967e+112	6.853081242536654e+112	5.174676155214135e+112
2	-9.893319725742429e-275	-9.099256253469455e-275	-9.198514187503577e-275
9	-1.7523220282583258e+27	-2.534584590737501e+21	-1.7289388930153844e+27

Iters

Range

Point

5.062782482725967e+112

6.853081242536654e+112

5.174676155214135e+112

-9.893319725742429e-275

-9.099256253469455e-275

-9.198514187503577e-275

-1.7523220282583258e+27

-2.534584590737501e+21

-1.7289388930153844e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

210.0ms	1057×	body	2560	valid
196.0ms	5833×	body	80	valid
148.0ms	878×	body	1280	valid
90.0ms	2890×	body	80	nan
57.0ms	458×	body	640	valid
34.0ms	138×	body	5120	valid
25.0ms	245×	body	320	valid
9.0ms	97×	body	160	valid