Details

Time bar (total: 5.9s)

sample62.0ms

Algorithm
intervals
Results
14.0ms183×body80valid
12.0ms33×body2560valid
10.0ms31×body1280valid
6.0ms85×body80nan
4.0ms17×body640valid
2.0ms9×body320valid
0.0ms1×body5120valid
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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(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:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(+ (- 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)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune312.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

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))
31.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* (* 4.0 a) c))
193.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify124.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
06742663
134622412
250012406

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
15.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

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:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06103042
130781945
250021857

prune341.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
132×add-sqr-sqrt
131×*-un-lft-identity
123×add-cube-cbrt
95×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
36×add-exp-log
22×add-cbrt-cube
19×neg-mul-1
17×prod-exp
11×frac-times fma-neg
10×pow1 add-log-exp
9×cbrt-unprod
8×flip3-- div-exp flip--
7×associate-*r* associate-*l/
5×associate-*r/
4×cbrt-undiv expm1-log1p-u sub-neg log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log pow-prod-down un-div-inv
2×rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 295
Calls
4 calls:
69.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (- 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)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010999218
150015868

prune414.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

regimes178.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 30.0b

bsearch248.0ms

Steps
ItersRangePoint
8
3.182319375801986e+130
1.3165557463351014e+133
3.29571176074688e+130
11
-2.847532546532628e-300
1.5391744236734674e-294
-1.0623739899498678e-305
7
-2.129980745276144e+116
-9.287529331322677e+113
-9.597540061084627e+115

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05631
16931
27331
37531
47531

end0.0ms

sample1.8s

Algorithm
intervals
Results
443.0ms5876×body80valid
409.0ms1068×body2560valid
276.0ms882×body1280valid
209.0ms2898×body80nan
110.0ms446×body640valid
47.0ms103×body5120valid
41.0ms220×body320valid
15.0ms115×body160valid