Details

Time bar (total: 6.2s)

sample68.0ms

Algorithm
intervals
Results
16.0ms33×body2560valid
14.0ms183×body80valid
10.0ms31×body1280valid
6.0ms85×body80nan
4.0ms17×body640valid
2.0ms9×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite63.0ms

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:
40.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0438854
11702750
25001735

prune351.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
203.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
06742663
134622412
250012406

prune519.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
15.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
56.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06103042
130781945
250021857

prune357.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
144×add-sqr-sqrt
138×*-un-lft-identity
130×add-cube-cbrt
95×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
13×associate-*l*
11×fma-neg
10×times-frac add-log-exp
9×add-exp-log add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sqrt-div associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 289
Calls
4 calls:
67.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify131.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
09278466
135705475
250025159

prune427.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

regimes132.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 30.0b

bsearch272.0ms

Steps
ItersRangePoint
8
3.182319375801986e+130
1.3165557463351014e+133
3.29571176074688e+130
11
-2.847532546532628e-300
1.5391744236734674e-294
-1.0623739899498678e-305
7
-2.129980745276144e+116
-9.287529331322677e+113
-9.597540061084627e+115

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05328
16428
26828
36828

end0.0ms

sample1.8s

Algorithm
intervals
Results
448.0ms5876×body80valid
408.0ms1068×body2560valid
275.0ms882×body1280valid
219.0ms2898×body80nan
109.0ms446×body640valid
51.0ms103×body5120valid
41.0ms220×body320valid
15.0ms115×body160valid