Details

Time bar (total: 6.0s)

sample74.0ms

Algorithm
intervals
Results
17.0ms47×body2560valid
17.0ms167×body80valid
10.0ms32×body1280valid
8.0ms107×body80nan
4.0ms16×body640valid
2.0ms4×body5120valid
2.0ms9×body320valid
1.0ms6×body160valid

simplify12.0ms

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: 35.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.6b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(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:
36.0ms
(/ (+ (- 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)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0438854
11658750
25001735

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify109.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
06652663
132592412
250012405

prune418.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.6b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
9.2b
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
256×add-sqr-sqrt
255×*-un-lft-identity
159×add-cube-cbrt
154×add-exp-log
117×associate-/l*
94×div-exp
72×add-cbrt-cube
48×distribute-lft-out-- difference-of-squares
40×cbrt-undiv
30×prod-exp
27×sqrt-prod
24×distribute-rgt-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp 1-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div div-sub clear-num associate-/r* associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 348
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
65.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
41.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series356.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
128.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
109.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
017576116
150025494

prune773.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
13.0b
(/ (* a c) a)
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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 associate-/r* flip--
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 cbrt-unprod div-inv associate-/l*
Counts
4 → 146
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(/ (* a c) a)
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series203.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
6.0ms
(/ (* a c) a)
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05002930
119761883
250011788

prune310.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

regimes185.0ms

Accuracy

94.3% (1.4b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.2b

bsearch148.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
3.6708609126801744e+125
4
-1.3699538778299852e-160
-8.754296253605712e-161
-8.908835082502404e-161
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-2.3202538172935113e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04929
14929

end0.0ms

sample1.8s

Algorithm
intervals
Results
454.0ms5747×body80valid
410.0ms1108×body2560valid
283.0ms926×body1280valid
197.0ms2804×body80nan
115.0ms481×body640valid
47.0ms106×body5120valid
41.0ms215×body320valid
15.0ms117×body160valid