Details

sample310.0ms

Algorithm

intervals

Results

15.0ms	181×	body	80	valid
12.0ms	38×	body	2560	valid
8.0ms	31×	body	1280	valid
4.0ms	66×	body	80	nan
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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:

33.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

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

prune294.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

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:

18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (98.0ms)

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

prune581.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.2b	(/ a (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`add-cube-cbrt`
43×	`add-exp-log`
34×	`sqrt-prod`
23×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`div-exp`
13×	`prod-exp`
10×	`fma-neg`
8×	`pow1` `cbrt-undiv` `add-log-exp`
7×	`neg-mul-1`
6×	`times-frac` `associate-/l*`
5×	`associate-/r/` `cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `flip--` `log1p-expm1-u`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-*l/` `inv-pow`

Counts

4 → 173

Calls

4 calls:

35.0ms	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ a (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	671	3001
1	2800	1905
2	5002	1851

prune294.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 170

Calls

4 calls:

23.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	505	3034
1	1685	2122
2	5002	2035

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.8b

regimes174.0ms

Accuracy

96.7% (0.8b remaining)

Error of 6.7b against oracle of 5.9b and baseline of 29.9b

bsearch200.0ms

Steps

Iters	Range	Point
10	9.168682727753708e+124	1.4581761209996442e+140	9.792086348653723e+126
10	7.390461352903605e-258	6.899183211307731e-244	7.484772368654571e-258
8	-4.003837004793086e+154	-2.2826144912851317e+150	-1.9721792334777768e+151

Iters

Range

Point

9.168682727753708e+124

1.4581761209996442e+140

9.792086348653723e+126

7.390461352903605e-258

6.899183211307731e-244

7.484772368654571e-258

-4.003837004793086e+154

-2.2826144912851317e+150

-1.9721792334777768e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

434.0ms	5832×	body	80	valid
351.0ms	1078×	body	2560	valid
232.0ms	858×	body	1280	valid
184.0ms	2694×	body	80	nan
101.0ms	461×	body	640	valid
38.0ms	223×	body	320	valid
37.0ms	96×	body	5120	valid
14.0ms	105×	body	160	valid