Details

Time bar (total: 3.9s)

sample45.0ms

Algorithm
intervals
Results
10.0ms43×body2560valid
7.0ms178×body80valid
6.0ms84×body80nan
5.0ms26×body1280valid
2.0ms14×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

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:
18.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05903305
121012212
250022128

prune339.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

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:
15.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify93.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06563422
125942238
250012193

prune323.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

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:
12.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series371.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05463278
120652181
250022098

prune314.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.4b

regimes195.0ms

Accuracy

81.8% (5.2b remaining)

Error of 10.5b against oracle of 5.3b and baseline of 33.7b

bsearch109.0ms

Steps
ItersRangePoint
9
8.465625442272063e+58
8.825425083170634e+65
3.295450950813408e+65
7
-8.900046045436026e-13
-1.901214192353153e-14
-1.3295118613703302e-13

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.2s

Algorithm
intervals
Results
254.0ms1040×body2560valid
239.0ms5928×body80valid
184.0ms903×body1280valid
113.0ms2982×body80nan
68.0ms437×body640valid
31.0ms108×body5120valid
24.0ms213×body320valid
11.0ms110×body160valid