Details

Time bar (total: 8.3s)

sample88.0ms

Algorithm
intervals
Results
20.0ms525×pre80true
19.0ms146×body160valid
18.0ms269×body80nan
8.0ms47×body320valid
4.0ms63×body80valid

simplify11.0ms

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: 43.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 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:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735

prune273.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
197.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify154.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08325099
139673830
250013828

prune596.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.6b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 217
Calls
4 calls:
84.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
4.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series499.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
194.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
50.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
100.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify158.0ms

Algorithm
egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
08804267
145663879
250013878

prune729.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))) (* 2.0 a))
0.3b
(/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))
0.6b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
484×add-sqr-sqrt
316×*-un-lft-identity
220×add-cube-cbrt
165×associate-/l*
155×add-exp-log
144×difference-of-squares
120×sqrt-prod
108×cbrt-prod
94×div-exp
73×add-cbrt-cube
48×distribute-lft-out--
40×cbrt-undiv
30×unpow-prod-down cube-prod prod-exp
26×sqr-pow
24×distribute-rgt-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp 1-exp
5×pow1
4×cube-div expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult cbrt-div flip3-- frac-2neg unpow3 div-sub clear-num associate-/r* associate-/r/ flip-- associate-/l/
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 463
Calls
4 calls:
113.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))) (* 2.0 a))
82.0ms
(/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))
4.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series394.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))) (* 2.0 a))
113.0ms
(/ (/ (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))) 4.0) (* a c))
50.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
101.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify119.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
023699268
150018743

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
12815

end0.0ms

sample2.4s

Algorithm
intervals
Results
629.0ms4877×body160valid
546.0ms8331×body80nan
495.0ms16331×pre80true
246.0ms1351×body320valid
125.0ms1772×body80valid