Details

Time bar (total: 5.9s)

sample51.0ms

Algorithm
intervals
Results
10.0ms37×body2560valid
10.0ms196×body80valid
6.0ms28×body1280valid
4.0ms91×body80nan
2.0ms12×body640valid
1.0ms5×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b
(- (* b b) (* (* 3.0 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms
(- (* b b) (* (* 3.0 a) c))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
41.0ms
(- (* b b) (* (* 3.0 a) c))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0433855
11670751
25001736

prune273.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.5b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
143.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
168.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify139.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08255119
137383863
250013860

prune516.0ms

Filtered
244 candidates to 141 candidates (57.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
7.9b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
54×add-cbrt-cube
48×add-cube-cbrt
40×div-exp
36×sqrt-prod
30×prod-exp
24×distribute-rgt-neg-in
22×cbrt-undiv
21×distribute-lft-neg-in
16×cbrt-unprod
10×fma-neg
8×times-frac 1-exp associate-/l* add-log-exp
7×neg-mul-1
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 185
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
43.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
117.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
09464085
145602694
250012692

prune340.0ms

Filtered
197 candidates to 93 candidates (47.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
7.9b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
220×add-sqr-sqrt
219×*-un-lft-identity
159×add-cube-cbrt
60×prod-diff
48×sqrt-prod
45×associate-/l*
36×distribute-rgt-neg-in
30×distribute-lft-out-- difference-of-squares
23×add-exp-log add-cbrt-cube
21×distribute-lft-neg-in
18×div-inv
11×cbrt-undiv div-exp
10×fma-neg
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 317
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
123.0ms
(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
107.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013396702
150015506

prune844.0ms

Filtered
329 candidates to 205 candidates (62.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

regimes277.0ms

Accuracy

94.8% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.5b

bsearch167.0ms

Steps
ItersRangePoint
8
2.531505514381809e+64
5.72577144612764e+68
2.4235533085097852e+67
9
-4.626257585305123e-261
-5.136473888129245e-268
-7.086437297855376e-264
7
-4.788437381304621e+112
-1.2414549986870086e+111
-2.8688546137715554e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04930
15130
25130

end0.0ms

sample1.1s

Algorithm
intervals
Results
249.0ms1121×body2560valid
223.0ms5763×body80valid
150.0ms856×body1280valid
101.0ms2821×body80nan
62.0ms452×body640valid
34.0ms128×body5120valid
26.0ms252×body320valid
8.0ms122×body160valid