Details

Time bar (total: 5.2s)

sample35.0ms

Algorithm
intervals
Results
7.0ms209×body80valid
7.0ms34×body2560valid
4.0ms22×body1280valid
3.0ms79×body80nan
2.0ms18×body640valid
0.0ms4×body160valid
0.0ms3×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite58.0ms

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:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
41.0ms
(- (* b b) (* (* 3.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0433855
11670751
25001736

prune286.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
4.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.6b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite85.0ms

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) (* (* 3.0 a) c))
45.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* b b) (* (* 3.0 a) c))
217.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
181.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify120.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
06692663
134312412
250012406

prune461.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma b b (- 0 (* 3.0 (* a c))))
4.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
10.6b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c)))))))
23.5b
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

rewrite69.0ms

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/
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×flip3-- flip-- associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 150
Calls
4 calls:
0.0ms
(fma b b (- 0 (* 3.0 (* a c))))
34.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
27.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c)))))))
2.0ms
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(fma b b (- 0 (* 3.0 (* a c))))
145.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))) (* 3.0 a))
175.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c)))))))
77.0ms
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05902576
126512329
250012312

prune435.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))
1.5b
(fma b b (- 0 (* 3.0 (* a c))))
14.2b
(/ (* 3.0 a) (* 3.0 (* a c)))
23.5b
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
60×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
10×fma-neg
9×prod-exp cbrt-unprod
8×add-log-exp
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square flip3-- frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* flip-- fma-udef div-inv associate-/l*
Counts
4 → 142
Calls
4 calls:
11.0ms
(- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))
0.0ms
(fma b b (- 0 (* 3.0 (* a c))))
7.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
1.0ms
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

series227.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (- b) (sqrt (fma b b (- 0 (* 3.0 (* a c))))))
53.0ms
(fma b b (- 0 (* 3.0 (* a c))))
11.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
77.0ms
(sqrt (fma b b (- 0 (* 3.0 (* a c)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05232954
123491842
250021735

prune269.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes354.0ms

Accuracy

94.1% (1.4b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.5b

bsearch194.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
1.8676563684114658e+102
11
-6.180552121099898e-304
6.534853956177064e-292
1.0719826190049434e-308
10
-3.0823188855845346e+100
-4.9258557020066e+89
-7.478383220944118e+90

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05528
16528
27128
37228
47428
57428

end0.0ms

sample1.1s

Algorithm
intervals
Results
223.0ms1070×body2560valid
208.0ms5838×body80valid
154.0ms884×body1280valid
102.0ms2849×body80nan
68.0ms497×body640valid
26.0ms102×body5120valid
22.0ms219×body320valid
7.0ms104×body160valid