Details

Time bar (total: 5.2s)

sample81.0ms

Algorithm
intervals
Results
22.0ms188×body80valid
15.0ms32×body2560valid
10.0ms25×body1280valid
9.0ms91×body80nan
5.0ms17×body640valid
3.0ms6×body5120valid
2.0ms7×body320valid
1.0ms3×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- 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)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×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 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
41.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
5.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05903306
121012212
250022128

prune335.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×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 times-frac associate-/r*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
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 → 156
Calls
4 calls:
21.0ms
(/ (* 2.0 a) (- (- 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))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05463278
120652181
250022098

prune327.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
53.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify81.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06563422
125942238
250012193

prune315.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.2b

regimes175.0ms

Accuracy

84% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.4b

bsearch156.0ms

Steps
ItersRangePoint
8
5.408584085660923e+89
1.6744273082514658e+93
2.8046284917653458e+91
9
-4.531045936315461e-35
-5.36339357665534e-42
-5.4278904486834676e-42

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03616
13616

end0.0ms

sample2.3s

Algorithm
intervals
Results
597.0ms5792×body80valid
509.0ms1041×body2560valid
372.0ms916×body1280valid
269.0ms2838×body80nan
157.0ms481×body640valid
65.0ms250×body320valid
63.0ms107×body5120valid
19.0ms107×body160valid