Details

Time bar (total: 5.0s)

sample279.0ms

Algorithm
intervals
Results
9.0ms35×body2560valid
6.0ms186×body80valid
4.0ms25×body1280valid
3.0ms82×body80nan
2.0ms8×body5120valid
2.0ms13×body640valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify13.0ms

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: 33.0b

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))))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

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:
41.0ms
(/ (+ (- 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))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune308.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.6b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

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))))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
09195579
139184508
250014505

prune595.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0b
(/ a (* a c))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

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 flip-- associate-/l*
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 associate-/r* cbrt-unprod div-inv
Counts
4 → 146
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(/ a (* a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(/ a (* a c))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04732542
116021646
250011557

prune273.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.1b
(* (/ (* (cbrt a) (cbrt a)) a) (/ (cbrt a) c))
24.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
65×*-un-lft-identity
61×add-cube-cbrt prod-diff
34×sqrt-prod
28×times-frac
25×add-exp-log
22×distribute-rgt-neg-in associate-*r*
21×distribute-lft-neg-in
18×add-cbrt-cube
11×cbrt-prod fma-neg
10×add-log-exp
8×prod-exp cbrt-unprod
7×pow1 cbrt-undiv neg-mul-1 div-exp associate-*l*
6×unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div div-inv distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 184
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms
(* (/ (* (cbrt a) (cbrt a)) a) (/ (cbrt a) c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series178.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms
(* (/ (* (cbrt a) (cbrt a)) a) (/ (cbrt a) c))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07813071
133532108
250011953

prune412.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes271.0ms

Accuracy

92% (2.0b remaining)

Error of 7.4b against oracle of 5.4b and baseline of 30.6b

bsearch96.0ms

Steps
ItersRangePoint
0
3459389182982077.0
3464539799267021.5
3461964491124549.0
7
2.0585255055480137e-204
5.114354928139511e-203
5.21257241609852e-204
11
-1.1860998636736231e+119
-1.6133553378404837e+99
-3.7171108546007633e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05442
15442

end0.0ms

sample1.0s

Algorithm
intervals
Results
215.0ms1075×body2560valid
197.0ms5830×body80valid
145.0ms900×body1280valid
98.0ms2959×body80nan
57.0ms457×body640valid
24.0ms253×body320valid
22.0ms92×body5120valid
8.0ms122×body160valid