Details

Time bar (total: 5.3s)

sample47.0ms

Algorithm
intervals
Results
8.0ms32×body2560valid
8.0ms179×body80valid
7.0ms110×body80nan
7.0ms36×body1280valid
2.0ms10×body640valid
1.0ms12×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b
(+ (- 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)))

rewrite32.0ms

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:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(+ (- 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)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25001735

prune301.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
4.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
06742663
134622412
250012406

prune449.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.2b
(+ (- 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)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
48×*-un-lft-identity
29×add-sqr-sqrt
28×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×fma-def distribute-lft-out add-log-exp
9×associate-/r/
8×distribute-rgt-neg-in
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 134
Calls
4 calls:
13.0ms
(/ 1 (/ (* 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))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05561665
127071442
250011371

prune303.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.2b
(+ (- 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)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
333×times-frac
224×*-un-lft-identity
125×add-sqr-sqrt
124×add-cube-cbrt
87×add-exp-log
58×div-exp
50×distribute-lft-out
31×div-inv
28×distribute-rgt-neg-in
25×add-cbrt-cube
21×associate-/r*
17×associate-/r/
15×rec-exp 1-exp
13×cbrt-undiv
12×prod-exp
10×fma-def add-log-exp
9×flip3-+ flip-+
7×associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×flip3-- sqrt-div sum-log flip-- cbrt-unprod
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log clear-num associate-/l/
Counts
4 → 283
Calls
4 calls:
19.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(+ (- 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)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011424786
150014210

prune475.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.5b

regimes221.0ms

Accuracy

87.1% (3.4b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 32.3b

bsearch172.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
1026034526.7184467
7
7.34802909125151e-147
4.2494272563886066e-145
3.4709388758775547e-146
9
-3.2701742958179892e+66
-3.862137329617324e+60
-1.0461303908572575e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04929
15129
25129

end0.0ms

sample1.2s

Algorithm
intervals
Results
273.0ms1095×body2560valid
247.0ms5839×body80valid
190.0ms934×body1280valid
114.0ms2928×body80nan
77.0ms449×body640valid
30.0ms101×body5120valid
28.0ms235×body320valid
8.0ms101×body160valid