Details

Time bar (total: 8.9s)

sample308.0ms

Algorithm
intervals
Results
16.0ms188×body80valid
13.0ms31×body2560valid
10.0ms30×body1280valid
10.0ms91×body80nan
4.0ms15×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
1.0ms6×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b
(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:
34.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (+ (- 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))))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753

prune302.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

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:
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
27.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
138.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
167.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09195579
139184508
250014505

prune600.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

8.0b
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
9.5b
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
20.5b
(sqrt (- (* b_2 b_2) (* a c)))
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
8×add-log-exp
6×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
5×difference-of-squares
4×expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
3×associate-/l*
2×neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 108
Calls
4 calls:
8.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
173.0ms
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04511972
118901604
250011541

prune391.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.2b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1872×add-sqr-sqrt
1871×*-un-lft-identity
1387×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
154×sqrt-prod
142×distribute-rgt-neg-in
60×prod-diff
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
13×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1226
Calls
4 calls:
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
110.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
114.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify276.0ms

Algorithm
egg-herbie
Counts
1238 → 1238
Iterations

Useful iterations: 1 (67.0ms)

IterNodesCost
0446926937
1500125693

prune2.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes215.0ms

Accuracy

83.2% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 32.6b

bsearch114.0ms

Steps
ItersRangePoint
8
2.3682374127768157e-71
9.144612143045527e-68
1.1752867948836086e-69
7
-1.2511146020293208e+129
-2.5570389401985865e+127
-4.032376794487168e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03221
13221

end0.0ms

sample2.0s

Algorithm
intervals
Results
521.0ms5911×body80valid
431.0ms1058×body2560valid
283.0ms848×body1280valid
224.0ms2843×body80nan
127.0ms460×body640valid
45.0ms222×body320valid
45.0ms93×body5120valid
21.0ms131×body160valid