Details

Time bar (total: 5.5s)

sample46.0ms

Algorithm
intervals
Results
9.0ms42×body2560valid
7.0ms193×body80valid
6.0ms16×body1280valid
4.0ms99×body80nan
2.0ms17×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.3b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

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:
62.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11658750
25001735

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
4.4b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite165.0ms

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:
9.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series679.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* a c)))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
402.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify108.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06652663
132592412
250012405

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
10.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.1b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
8×add-log-exp
6×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
5×difference-of-squares
4×expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
3×associate-/l*
2×neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 108
Calls
4 calls:
32.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
83.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04572299
119781877
250011812

prune407.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
15.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
20.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

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:
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify84.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
05973033
128321946
250021857

prune286.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes195.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.8b

bsearch146.0ms

Steps
ItersRangePoint
7
2.5938763934072053e+128
6.455437820905187e+129
4.0598649397170545e+128
6
-2.891186526843327e-238
-3.8162486351435958e-239
-5.269237409668851e-239
7
-3.11898899158337e+65
-2.3526715177838076e+63
-3.0609761389176743e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05037
15237
25237

end0.0ms

sample1.2s

Algorithm
intervals
Results
231.0ms5908×body80valid
230.0ms1025×body2560valid
151.0ms843×body1280valid
111.0ms2941×body80nan
69.0ms457×body640valid
32.0ms119×body5120valid
24.0ms228×body320valid
7.0ms101×body160valid