Details

Time bar (total: 4.8s)

sample48.0ms

Algorithm
intervals
Results
8.0ms196×body80valid
8.0ms31×body2560valid
7.0ms113×body80nan
6.0ms32×body1280valid
1.0ms11×body320valid
1.0ms7×body640valid
1.0ms4×body5120valid
0.0ms1×body160valid

simplify17.0ms

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: 36.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(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:
16.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms
(- (- 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))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05903305
121012212
250022128

prune363.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(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-/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))))))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05463278
120652181
250022098

prune344.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

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:
20.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06563422
125942238
250012193

prune353.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* a c)))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 67
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series266.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0170564
1622537
22864531
35001524

prune316.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.1b

regimes228.0ms

Accuracy

82.3% (5.1b remaining)

Error of 10.7b against oracle of 5.7b and baseline of 34.3b

bsearch85.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2445759453.473797
6
-1.6265262117742566e-90
-1.5703225997493665e-91
-1.3933893531775335e-90

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03616
13616

end0.0ms

sample1.2s

Algorithm
intervals
Results
280.0ms1087×body2560valid
246.0ms5898×body80valid
172.0ms838×body1280valid
116.0ms2921×body80nan
68.0ms436×body640valid
37.0ms121×body5120valid
27.0ms230×body320valid
9.0ms116×body160valid