Details

Time bar (total: 5.2s)

sample40.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
6.0ms31×body1280valid
5.0ms21×body2560valid
4.0ms103×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438855
11702750
25001735

prune317.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log
16×add-cbrt-cube
12×*-un-lft-identity
10×fma-def add-log-exp
9×add-sqr-sqrt
8×add-cube-cbrt
7×prod-exp
6×div-exp
5×pow1
4×cbrt-undiv expm1-log1p-u distribute-rgt-neg-in cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×flip3-- flip3-+ sqrt-div 1-exp associate-*r/ sum-log flip-- flip-+ associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 fma-neg diff-log prod-diff neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
19.0ms
(/ (* 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (* 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0500860
12420722
25003707

prune281.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
48×*-un-lft-identity
29×add-sqr-sqrt
28×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×fma-def distribute-lft-out add-log-exp
9×associate-/r/
8×distribute-rgt-neg-in
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 134
Calls
4 calls:
28.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify75.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05561665
127071442
250011371

prune327.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify161.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
08295119
137633863
250013860

prune549.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

regimes183.0ms

Accuracy

86.7% (3.8b remaining)

Error of 9.3b against oracle of 5.5b and baseline of 34.1b

bsearch167.0ms

Steps
ItersRangePoint
2
3.9431530817676045e+109
4.557375181159837e+109
4.019930844191633e+109
9
8.821301774413145e-82
2.0920398247873342e-75
8.930527750856993e-82
10
-1.5405955983178716e+163
-1.402598515452623e+153
-2.3044033969831823e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05348
15548
25548

end0.0ms

sample1.2s

Algorithm
intervals
Results
256.0ms1101×body2560valid
236.0ms5850×body80valid
176.0ms921×body1280valid
112.0ms2888×body80nan
70.0ms450×body640valid
31.0ms228×body320valid
29.0ms103×body5120valid
9.0ms121×body160valid