Details

Time bar (total: 5.1s)

sample283.0ms

Algorithm
intervals
Results
7.0ms33×body1280valid
7.0ms35×body2560valid
6.0ms181×body80valid
3.0ms92×body80nan
2.0ms17×body640valid
1.0ms6×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.0b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
23.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753

prune301.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
11.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
134.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
164.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
09195579
139184508
250014505

prune588.0ms

Filtered
296 candidates to 172 candidates (58.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b
(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
110×*-un-lft-identity
76×add-cube-cbrt
60×prod-diff
58×times-frac
41×sqrt-prod
29×distribute-rgt-neg-in
28×add-exp-log
27×associate-*l*
21×distribute-lft-neg-in
18×add-cbrt-cube
16×distribute-lft-out-- difference-of-squares
13×associate-*r*
10×fma-neg
9×div-exp
8×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-/r*
6×unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u flip3-- associate-/r/ flip-- cbrt-unprod log1p-expm1-u
3×div-inv associate-/l*
2×rec-exp sqrt-div diff-log 1-exp associate-/l/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 229
Calls
4 calls:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms
(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
14.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms
(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
163.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08894144
139593028
250013027

prune467.0ms

Filtered
241 candidates to 137 candidates (56.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.1b
(/ (* a c) a)
23.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- times-frac diff-log associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 146
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(/ (* a c) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series165.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(/ (* a c) a)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04802538
118441650
250021553

prune277.0ms

Filtered
158 candidates to 82 candidates (51.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes178.0ms

Accuracy

87.8% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.5b

bsearch71.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
5.174676155214135e+112
2
-9.893319725742429e-275
-9.099256253469455e-275
-9.198514187503577e-275
9
-1.7523220282583258e+27
-2.534584590737501e+21
-1.7289388930153844e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14726
24726

end0.0ms

sample1.0s

Algorithm
intervals
Results
207.0ms1057×body2560valid
200.0ms5833×body80valid
142.0ms878×body1280valid
90.0ms2890×body80nan
56.0ms458×body640valid
33.0ms138×body5120valid
23.0ms245×body320valid
6.0ms97×body160valid