Details

Time bar (total: 5.0s)

sample43.0ms

Algorithm
intervals
Results
7.0ms32×body2560valid
7.0ms184×body80valid
6.0ms29×body1280valid
4.0ms94×body80nan
3.0ms21×body640valid
2.0ms6×body5120valid
1.0ms8×body320valid
0.0ms4×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: 35.7b

localize15.0ms

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)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

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:
46.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

series286.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05903305
121012212
250022128

prune341.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite89.0ms

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:
58.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series286.0ms

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)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06563422
125942238
250012193

prune326.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

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)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

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:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(- (- 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))))

series286.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05903305
121012212
250022128

prune311.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

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:
26.0ms
(/ 1 (/ (* 2.0 a) (- (- 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))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
248.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
88.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify94.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07184221
130992976
250012863

prune346.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes277.0ms

Accuracy

80.4% (5.6b remaining)

Error of 11.0b against oracle of 5.4b and baseline of 34.0b

bsearch199.0ms

Steps
ItersRangePoint
8
9.456042252142157e+48
5.633410846004884e+51
5.5792500737545097e+51
7
-8.729222821301493e-116
-3.4297016692569784e-117
-8.637249247672526e-116
5
-2.4989029931801306e-33
-1.2234821552231479e-33
-2.374474662067348e-33
9
-2.416358248243101e+20
-517129303899.1912
-524848456042.2247

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04529
15129
25129

end0.0ms

sample1.2s

Algorithm
intervals
Results
239.0ms5915×body80valid
238.0ms1029×body2560valid
183.0ms918×body1280valid
105.0ms2875×body80nan
67.0ms457×body640valid
29.0ms101×body5120valid
24.0ms196×body320valid
10.0ms131×body160valid