Details

Time bar (total: 5.6s)

sample45.0ms

Algorithm
intervals
Results
8.0ms32×body2560valid
8.0ms179×body80valid
7.0ms36×body1280valid
4.0ms110×body80nan
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))))

rewrite33.0ms

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:
15.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(+ (- 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))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
51.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11658750
25001735

prune491.0ms

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))))

rewrite46.0ms

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)))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06652663
132592412
250012405

prune452.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize19.0ms

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))))

rewrite35.0ms

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)))))))
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))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05561665
126641442
250021371

prune332.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

localize22.0ms

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))))

rewrite53.0ms

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)))))))
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))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
85.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011424786
150024210

prune534.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.5b

regimes233.0ms

Accuracy

87.1% (3.4b remaining)

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

bsearch175.0ms

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
04529
14729
24729

end0.0ms

sample1.2s

Algorithm
intervals
Results
279.0ms1095×body2560valid
257.0ms5839×body80valid
191.0ms934×body1280valid
118.0ms2928×body80nan
71.0ms449×body640valid
31.0ms101×body5120valid
28.0ms235×body320valid
10.0ms101×body160valid