Details

Time bar (total: 5.6s)

sample284.0ms

Algorithm
intervals
Results
7.0ms184×body80valid
5.0ms34×body1280valid
5.0ms25×body2560valid
3.0ms115×body80nan
2.0ms9×body5120valid
2.0ms15×body640valid
1.0ms10×body320valid
0.0ms5×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: 35.9b

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))
1.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

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:
66.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
31.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite203.0ms

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:
32.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
84.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
58.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
128.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
151.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify139.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09195579
139184508
250014505

prune585.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.8b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.5b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
162×times-frac
118×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
32×add-exp-log
28×associate-/r*
26×distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
21×distribute-lft-neg-in
16×div-exp
10×cbrt-undiv fma-neg
8×add-log-exp
7×neg-mul-1
6×prod-exp div-inv
5×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log associate-/r/ associate-/l/
Counts
4 → 258
Calls
4 calls:
32.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
41.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
159.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
135.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09864682
143183613
250013595

prune493.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.4b
(- (* b_2 b_2) (* a c))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
66×*-un-lft-identity
62×add-cube-cbrt
61×prod-diff
34×sqrt-prod
33×times-frac
32×add-exp-log
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
17×div-exp
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
7×neg-mul-1 1-exp associate-/r*
6×pow1 prod-exp
5×cbrt-undiv div-inv
4×expm1-log1p-u rec-exp log1p-expm1-u
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ cbrt-unprod inv-pow
Counts
4 → 184
Calls
4 calls:
49.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
9.0ms
(- (* b_2 b_2) (* a c))
33.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
28.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07023223
127252180
250012099

prune275.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes139.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.4b

bsearch132.0ms

Steps
ItersRangePoint
9
1.7695728335377845e+74
3.738006738925262e+80
5.232488921342498e+79
11
-1.5799869936663156e-158
-6.164197719833672e-182
-6.278504568756145e-182
6
-3.413061301452514e+122
-2.3517657564579724e+121
-1.5254699676315931e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
14524
24524

end0.0ms

sample1.1s

Algorithm
intervals
Results
200.0ms1059×body2560valid
193.0ms5785×body80valid
138.0ms896×body1280valid
92.0ms2930×body80nan
58.0ms490×body640valid
26.0ms115×body5120valid
22.0ms228×body320valid
7.0ms122×body160valid