Details

Time bar (total: 8.7s)

sample90.0ms

Algorithm
intervals
Results
20.0ms263×body80nan
18.0ms105×body320valid
15.0ms519×pre80true
12.0ms96×body160valid
5.0ms20×body640valid
2.0ms35×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: 51.4b

localize11.0ms

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))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.9b
(+ (- 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))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25002735

prune233.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))))
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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series472.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify155.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune540.0ms

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

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
880×times-frac
425×add-sqr-sqrt *-un-lft-identity
277×add-cube-cbrt
198×add-exp-log
122×div-exp
120×associate-/l*
90×add-cbrt-cube
74×distribute-lft-out-- difference-of-squares
67×sqrt-prod
60×prod-diff
58×distribute-rgt-neg-in
51×cbrt-undiv
36×prod-exp
31×associate-/r*
27×div-inv
21×distribute-lft-neg-in
15×rec-exp 1-exp
14×cbrt-unprod
10×fma-neg
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num associate-/r/
2×diff-log div-sub associate-/l/
1×associate--l- neg-sub0 sub-neg flip3-- pow-flip neg-log flip-- inv-pow
Counts
4 → 559
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c)))
64.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
40.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))

series497.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
171.0ms
(/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c)))
131.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
117.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))

simplify130.0ms

Algorithm
egg-herbie
Counts
571 → 571
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0193011308
150019498

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
608×times-frac
325×*-un-lft-identity
185×add-sqr-sqrt
165×add-cube-cbrt
109×associate-/l*
80×distribute-lft-out--
54×add-exp-log
50×div-inv
48×distribute-rgt-neg-in
42×add-cbrt-cube
26×div-exp
20×distribute-rgt-out--
19×cbrt-undiv
18×distribute-lft-neg-in sqrt-prod
17×associate-/r*
12×associate-/r/
10×difference-of-squares
8×prod-exp
6×neg-mul-1 cbrt-unprod
5×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×rec-exp flip3-- 1-exp frac-sub flip-- associate-/l/ sub-div
2×div-sub distribute-frac-neg
1×neg-sub0 pow-flip inv-pow
Counts
4 → 365
Calls
4 calls:
130.0ms
(/ 1 (- (/ (/ (- b) 4.0) (* a c)) (/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c))))
13.0ms
(/ (/ (- b) 4.0) (* a c))
13.0ms
(/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c))
202.0ms
(/ (/ 1 (- (/ (/ (- b) 4.0) (* a c)) (/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c)))) (* 2.0 a))

series580.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ 1 (- (/ (/ (- b) 4.0) (* a c)) (/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c))))
29.0ms
(/ (/ (- b) 4.0) (* a c))
144.0ms
(/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c))
194.0ms
(/ (/ 1 (- (/ (/ (- b) 4.0) (* a c)) (/ (/ (sqrt (- (* b b) (* (* 4.0 a) c))) 4.0) (* a c)))) (* 2.0 a))

simplify80.0ms

Algorithm
egg-herbie
Counts
377 → 377
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015405558
150015036

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes93.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02916
13116
23116

end0.0ms

sample2.5s

Algorithm
intervals
Results
642.0ms3639×body320valid
519.0ms8232×body80nan
477.0ms16232×pre80true
366.0ms2934×body160valid
116.0ms500×body640valid
65.0ms927×body80valid