Details

Time bar (total: 5.6s)

sample40.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms189×body80valid
5.0ms25×body1280valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

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:
39.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0438854
11702750
25001735

prune339.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

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:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
165.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
203.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify152.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
08295119
137633863
250013860

prune627.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06103042
130781945
250021857

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
64×add-exp-log *-un-lft-identity
61×prod-diff
60×add-cube-cbrt
40×div-exp
34×sqrt-prod
31×times-frac
25×add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
15×1-exp
14×prod-exp
13×associate-/l*
11×cbrt-undiv fma-neg
10×add-log-exp
7×neg-mul-1
6×rec-exp
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 195
Calls
4 calls:
23.0ms
(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
55.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08453812
139292561
250012521

prune381.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

regimes240.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.2b against oracle of 5.3b and baseline of 29.8b

bsearch163.0ms

Steps
ItersRangePoint
5
5.10808278574109e+145
1.867402505400959e+146
5.540445008636524e+145
8
-1.2523555155265933e-243
-3.6841099953537603e-246
-3.72191682831812e-246
7
-2.963931757502914e+119
-3.3757792073266624e+117
-8.003368877449752e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04525
14525

end0.0ms

sample1.2s

Algorithm
intervals
Results
265.0ms1073×body2560valid
230.0ms5759×body80valid
183.0ms914×body1280valid
108.0ms2900×body80nan
68.0ms451×body640valid
29.0ms100×body5120valid
26.0ms229×body320valid
10.0ms132×body160valid