Details

Time bar (total: 4.8s)

sample40.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
7.0ms185×body80valid
5.0ms29×body1280valid
3.0ms97×body80nan
3.0ms19×body640valid
1.0ms3×body5120valid
0.0ms3×body320valid
0.0ms2×body160valid

simplify14.0ms

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: 31.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite134.0ms

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:
76.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series254.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
64.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms
(- (* b b) (* 4.0 (* a c)))
63.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05903306
121012212
250022128

prune317.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
49.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
60.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify93.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07184221
130992976
250012863

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite137.0ms

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:
76.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
70.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
60.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05903305
121012212
250022128

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite161.0ms

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:
102.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
69.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
38.0ms
(- (* b b) (* 4.0 (* a c)))
64.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06563422
125942238
250012193

prune307.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes227.0ms

Accuracy

84.5% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.3b

bsearch98.0ms

Steps
ItersRangePoint
10
8.043557394408689e+68
7.456819745307919e+79
7.351468977489713e+79
7
-1.316548984668948e-60
-1.056498470782689e-62
-2.8813430075089506e-61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03917
14317
24317

end0.0ms

sample1.2s

Algorithm
intervals
Results
240.0ms1070×body2560valid
217.0ms5935×body80valid
151.0ms857×body1280valid
106.0ms2993×body80nan
58.0ms425×body640valid
34.0ms121×body5120valid
23.0ms225×body320valid
8.0ms108×body160valid