Details

Time bar (total: 6.0s)

sample62.0ms

Algorithm
intervals
Results
14.0ms279×body80nan
11.0ms156×body160valid
10.0ms535×pre80true
5.0ms48×body320valid
2.0ms52×body80valid

simplify12.0ms

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: 44.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
39.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

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))
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438855
11702750
25002735

prune268.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

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))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify158.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08325099
139673830
250013828

prune571.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
312×add-exp-log
142×div-exp
138×add-cbrt-cube
137×prod-exp
121×prod-diff
102×add-sqr-sqrt
100×*-un-lft-identity
96×add-cube-cbrt
62×distribute-rgt-in distribute-lft-in
61×sqrt-prod
57×cbrt-unprod
48×cbrt-undiv
40×1-exp
37×distribute-rgt-neg-in
36×distribute-lft-neg-in
33×times-frac
16×rec-exp
14×associate-/l*
12×neg-mul-1
7×associate-*r*
6×pow1 add-log-exp
5×flip3-- associate-*l* associate-/r/ flip-- div-inv
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×sub-neg
2×frac-2neg associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×fma-neg diff-log pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 327
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
79.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
42.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
87.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
158.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify98.0ms

Algorithm
egg-herbie
Counts
339 → 339
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
016569136
150026441

prune444.0ms

Filtered
339 candidates to 102 candidates (30.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
327×add-exp-log
181×prod-diff
174×div-exp
144×add-sqr-sqrt *-un-lft-identity
136×add-cube-cbrt prod-exp
92×sqrt-prod
78×add-cbrt-cube
66×1-exp
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
36×rec-exp
31×times-frac
30×cbrt-undiv
27×cbrt-unprod
22×frac-times
19×neg-mul-1
14×associate-*l/ associate-/r/
13×associate-/l*
12×flip3-- flip--
11×fma-neg
10×associate-*r/ add-log-exp
9×pow1
7×associate-*r*
6×un-div-inv
4×expm1-log1p-u sub-neg log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log pow-prod-down div-inv
1×associate--l- neg-sub0 frac-2neg associate-*l* neg-log clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 414
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
40.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
182.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0175911251
150027362

prune505.0ms

Filtered
426 candidates to 131 candidates (30.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes117.0ms

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
02512
12512

end0.0ms

sample1.5s

Algorithm
intervals
Results
352.0ms4850×body160valid
312.0ms16117×pre80true
284.0ms8117×body80nan
143.0ms1343×body320valid
65.0ms1807×body80valid