Details

Time bar (total: 7.9s)

sample344.0ms

Algorithm
intervals
Results
8.0ms42×body2560valid
6.0ms193×body80valid
4.0ms99×body80nan
2.0ms16×body1280valid
2.0ms17×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize13.0ms

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))
1.3b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

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:
65.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune306.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
4.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* b_2 b_2) (* a c))
147.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
180.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07613434
134903258
250023250

prune532.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.4b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1827×add-sqr-sqrt
1826×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
240×distribute-lft-out-- difference-of-squares
123×sqrt-prod
120×distribute-rgt-neg-in
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 1152
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
131.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
95.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
121.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify245.0ms

Algorithm
egg-herbie
Counts
1164 → 1164
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0427624795
1500124124

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 196
Calls
4 calls:
53.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms
(- (* b_2 b_2) (* a c))
48.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
40.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06582519
129432155
250012004

prune306.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

regimes194.0ms

Accuracy

89.4% (2.8b remaining)

Error of 8.2b against oracle of 5.3b and baseline of 32.2b

bsearch137.0ms

Steps
ItersRangePoint
8
8.900017451179621e+70
5.1703700736353e+73
1.6498083831452493e+71
11
-1.026203141381591e-268
-2.600157470066103e-290
-2.4051364083326226e-287
7
-3.11898899158337e+65
-2.3526715177838076e+63
-3.0609761389176743e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04124
14124

end0.0ms

sample1.0s

Algorithm
intervals
Results
194.0ms5906×body80valid
189.0ms1024×body2560valid
128.0ms846×body1280valid
88.0ms2940×body80nan
53.0ms456×body640valid
29.0ms120×body5120valid
22.0ms230×body320valid
6.0ms100×body160valid