Details

Time bar (total: 6.4s)

sample53.0ms

Algorithm
intervals
Results
12.0ms516×pre80true
10.0ms150×body160valid
9.0ms260×body80nan
4.0ms106×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
29.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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)))
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- 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
25001735

prune263.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(- (* 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:
16.0ms
(- (- 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))
3.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
46.0ms
(- (* b b) (* (* 4.0 a) c))
184.0ms
(/ (+ 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 (114.0ms)

IterNodesCost
08325099
139673830
250013828

prune554.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
0.6b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp
6×associate-/r/
5×div-inv associate-/l/
4×expm1-log1p-u unpow-prod-down flip3-- flip-- log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
1×pow2 flip3-+ div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 241
Calls
4 calls:
93.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
62.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
18.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
30.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series550.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))))) (* 2.0 a))
229.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c))))))
98.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (fma b b (* (* 4.0 a) c)))
37.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09565104
150004587

prune763.0ms

Filtered
253 candidates to 150 candidates (59.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
102×*-un-lft-identity
70×add-cube-cbrt
61×prod-diff
51×add-exp-log
46×times-frac
38×sqrt-prod
29×distribute-rgt-neg-in
27×associate-*l* add-cbrt-cube
21×distribute-lft-neg-in
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
11×fma-neg
10×add-log-exp
8×cbrt-undiv cbrt-unprod
7×neg-mul-1 associate-*r* associate-/r*
6×pow1
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×diff-log div-inv associate-/l*
2×sub-neg associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times frac-2neg flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 226
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
63.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
181.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
145.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify175.0ms

Algorithm
egg-herbie
Counts
238 → 238
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09244824
147313436
250013436

prune494.0ms

Filtered
238 candidates to 127 candidates (53.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes126.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02212
12212

end0.0ms

sample1.4s

Algorithm
intervals
Results
315.0ms4482×body160valid
302.0ms16576×pre80true
285.0ms8576×body80nan
123.0ms3517×body80valid
0.0ms1×body320valid