Details

Time bar (total: 6.1s)

sample51.0ms

Algorithm
intervals
Results
10.0ms314×body80nan
10.0ms570×pre80true
9.0ms137×body160valid
4.0ms119×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: 27.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- 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

prune256.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* 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
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite99.0ms

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))
41.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify155.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune565.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg 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 → 230
Calls
4 calls:
1.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
30.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
11.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
19.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
87.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify129.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07675082
131663826
250013733

prune523.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
0.3b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
0.4b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
102×*-un-lft-identity
69×add-cube-cbrt
60×prod-diff
52×add-exp-log
45×times-frac
38×sqrt-prod
32×add-cbrt-cube
29×distribute-rgt-neg-in
27×associate-*r*
21×distribute-lft-neg-in
18×div-exp
17×prod-exp
16×distribute-lft-out-- difference-of-squares
10×cbrt-undiv fma-neg
9×cbrt-unprod
8×associate-/r* add-log-exp
7×pow1 neg-mul-1
6×associate-/l/
4×expm1-log1p-u frac-times rec-exp flip3-+ 1-exp associate-*l/ associate-/r/ flip-+ log1p-expm1-u associate-/l*
3×flip3-- associate-*l* flip-- div-inv unswap-sqr
2×frac-2neg diff-log associate-*r/ clear-num un-div-inv
1×associate--l- neg-sub0 sub-neg pow-flip pow-prod-down neg-log *-commutative inv-pow
Counts
4 → 234
Calls
4 calls:
13.0ms
(/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
15.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
14.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
38.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))
155.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))) (* 2.0 a))
86.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
190.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))

simplify192.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08874732
148333308
250013308

prune474.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02614
13814
24414
34414

end0.0ms

sample1.4s

Algorithm
intervals
Results
319.0ms4461×body160valid
293.0ms16802×pre80true
291.0ms8802×body80nan
124.0ms3538×body80valid
0.0ms1×body320valid