Details

Time bar (total: 5.2s)

sample39.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms196×body80valid
5.0ms28×body1280valid
3.0ms91×body80nan
2.0ms12×body640valid
1.0ms2×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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:
37.0ms
(/ (+ (- 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))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11658750
25001735

prune292.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
7.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite103.0ms

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)))))
45.0ms
(/ (/ (+ 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))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
360.0ms
(/ (/ (+ 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))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify131.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08185119
135603863
250013860

prune537.0ms

Filtered
244 candidates to 141 candidates (57.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0b
(/ (* 2.0 a) (* 4.0 (* a c)))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05973032
128321946
250021857

prune301.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
144×add-sqr-sqrt
138×*-un-lft-identity
130×add-cube-cbrt
95×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
13×associate-*l*
11×fma-neg
10×times-frac add-log-exp
9×add-exp-log add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sqrt-div associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 289
Calls
4 calls:
60.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify127.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
09288466
135295475
250025159

prune380.0ms

Filtered
301 candidates to 106 candidates (35.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

regimes167.0ms

Accuracy

81.6% (4.5b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 29.5b

bsearch81.0ms

Steps
ItersRangePoint
8
2.531505514381809e+64
5.72577144612764e+68
1.6161993363323858e+68
3
-2.3762030729656124e-61
-1.6676843733113775e-61
-1.889096466953326e-61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04419
15519
25919
35919

end0.0ms

sample1.1s

Algorithm
intervals
Results
247.0ms1122×body2560valid
222.0ms5762×body80valid
161.0ms856×body1280valid
97.0ms2821×body80nan
63.0ms449×body640valid
34.0ms128×body5120valid
26.0ms255×body320valid
9.0ms123×body160valid