Details

Time bar (total: 6.6s)

sample59.0ms

Algorithm
intervals
Results
13.0ms284×body80nan
10.0ms137×body160valid
10.0ms540×pre80true
4.0ms119×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: 28.4b

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))
28.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735

prune255.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (- 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)))))

rewrite187.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify149.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08325099
139673830
250013828

prune557.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.2b
(- (- 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))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite131.0ms

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)))))
19.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
58.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
41.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series532.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
91.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
159.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
198.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify121.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07675084
131663826
250013733

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))))
0.5b
(* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
66×sqrt-prod
54×times-frac
47×add-cube-cbrt *-un-lft-identity
32×sqrt-pow1
27×pow1
21×associate-/l*
20×add-exp-log add-cbrt-cube
16×pow1/2
15×swap-sqr
11×difference-of-squares
10×fma-neg prod-diff
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×add-log-exp
7×cbrt-undiv div-exp
6×distribute-lft-neg-in distribute-rgt-neg-in associate-/r/
5×pow-prod-down associate-/r* pow-sqr
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×prod-exp cbrt-unprod associate-/l/
2×neg-mul-1 frac-2neg diff-log clear-num
1×associate--l- pow2 neg-sub0 sub-neg flip3-+ pow-plus sqrt-unprod neg-log rem-square-sqrt *-commutative flip-+
Counts
4 → 209
Calls
4 calls:
15.0ms
(- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))
47.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))) (* 2.0 a))
32.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))))
20.0ms
(* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))
161.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c))))))))) (* 2.0 a))
198.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))))
87.0ms
(* (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))) (sqrt (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify140.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07584538
136413648
250023560

prune582.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes162.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02713
13413
24013
34013

end0.0ms

sample1.5s

Algorithm
intervals
Results
318.0ms4389×body160valid
310.0ms8772×body80nan
295.0ms16772×pre80true
136.0ms3610×body80valid
0.0ms1×body320valid