Details

Time bar (total: 7.4s)

sample117.0ms

Algorithm
intervals
Results
27.0ms278×body80nan
26.0ms110×body320valid
19.0ms534×pre80true
15.0ms90×body160valid
6.0ms20×body640valid
3.0ms36×body80valid

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: 51.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.5b
(+ (- 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))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25002735

prune246.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series455.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify154.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune550.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
121×prod-diff
92×add-cbrt-cube
90×add-sqr-sqrt
88×*-un-lft-identity
84×add-cube-cbrt
73×prod-exp
62×distribute-rgt-in distribute-lft-in
61×sqrt-prod
46×div-exp
41×cbrt-unprod
37×distribute-rgt-neg-in
36×distribute-lft-neg-in
26×cbrt-undiv
12×neg-mul-1
9×pow1
8×rec-exp 1-exp
7×associate-*r*
6×add-log-exp
5×flip3-- times-frac associate-*l* associate-/r/ flip--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u associate-/l*
3×sub-neg div-inv
2×pow-flip frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×fma-neg diff-log *-commutative inv-pow unswap-sqr
Counts
4 → 269
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
65.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
80.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
147.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
88.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
281 → 281
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012807983
150015713

prune391.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
87×add-exp-log
85×add-cbrt-cube
41×prod-exp cbrt-unprod
27×add-sqr-sqrt
26×associate-*r*
23×add-cube-cbrt *-un-lft-identity
20×div-exp
19×cbrt-undiv
15×times-frac
10×associate-*l*
9×pow1 distribute-lft-neg-in distribute-rgt-neg-in
8×sqrt-div associate-*l/ distribute-neg-frac
7×associate-/r/
6×sqrt-prod
5×frac-add associate-/r*
4×expm1-log1p-u frac-times flip3-- associate-*r/ flip-- log1p-expm1-u div-inv distribute-lft-out associate-/l* add-log-exp
2×neg-mul-1 frac-2neg pow-prod-down clear-num *-commutative distribute-rgt-neg-out unswap-sqr
1×rec-exp pow-flip flip3-+ 1-exp flip-+ inv-pow
Counts
4 → 167
Calls
4 calls:
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
51.0ms
(/ 1 (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
43.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
31.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- b))

series335.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
179.0ms
(/ 1 (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
125.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- b))

simplify47.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09582539
150012115

prune456.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes80.0ms

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
02713
12713

end0.0ms

sample3.2s

Algorithm
intervals
Results
867.0ms3656×body320valid
712.0ms8202×body80nan
579.0ms16202×pre80true
481.0ms2901×body160valid
150.0ms482×body640valid
90.0ms961×body80valid