Details

Time bar (total: 6.7s)

sample287.0ms

Algorithm
intervals
Results
8.0ms189×body80valid
7.0ms35×body2560valid
4.0ms25×body1280valid
3.0ms87×body80nan
1.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (* b_2 b_2) (* a c))
1.3b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
43.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753

prune303.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.3b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify136.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09195579
139184508
250014505

prune584.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.3b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
630×add-sqr-sqrt
629×*-un-lft-identity
433×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
82×sqrt-prod
70×distribute-rgt-neg-in
60×prod-diff
28×associate-/r*
22×div-inv
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×add-log-exp
7×neg-mul-1
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 569
Calls
4 calls:
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
178.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
154.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
581 → 581
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0175510832
150029428

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
1.0b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
569×add-sqr-sqrt
568×*-un-lft-identity
396×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
61×prod-diff
44×add-exp-log
43×div-inv
32×div-exp
29×associate-/r/
27×associate-/l*
21×distribute-lft-neg-in
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/r*
11×fma-neg
10×add-log-exp
8×cbrt-undiv rec-exp 1-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 548
Calls
4 calls:
46.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
35.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0196311056
150019439

prune711.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes188.0ms

Accuracy

93.5% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 29.8b

bsearch112.0ms

Steps
ItersRangePoint
6
4.706455236749836e+29
5.491842449186372e+30
5.349311795482947e+30
8
-1.2523555155265933e-243
-3.6841099953537603e-246
-6.7952690093112265e-245
7
-2.963931757502914e+119
-3.3757792073266624e+117
-5.955152059551362e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04023
14023

end0.0ms

sample987.0ms

Algorithm
intervals
Results
208.0ms1079×body2560valid
192.0ms5758×body80valid
148.0ms915×body1280valid
89.0ms2894×body80nan
54.0ms449×body640valid
23.0ms100×body5120valid
21.0ms223×body320valid
8.0ms133×body160valid