Details

Time bar (total: 5.6s)

sample41.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
8.0ms197×body80valid
5.0ms28×body1280valid
3.0ms90×body80nan
2.0ms13×body640valid
1.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

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: 34.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

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:
35.0ms
(/ (+ (- 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))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735

prune291.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

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))
46.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify129.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
06742663
134622412
250012406

prune461.0ms

Filtered
170 candidates to 117 candidates (68.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.7b
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
8.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
58×*-un-lft-identity
51×add-exp-log
46×times-frac
30×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp
14×distribute-lft-out-- difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 distribute-rgt-neg-in associate-*r* associate-/r*
6×add-log-exp
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 153
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify149.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
07662388
142302057
250012054

prune617.0ms

Filtered
165 candidates to 108 candidates (65.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
15.1b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

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 flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ 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 → 152
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
145.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06683371
134822161
250012072

prune304.0ms

Filtered
164 candidates to 82 candidates (50.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

regimes167.0ms

Accuracy

94.4% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.1b

bsearch179.0ms

Steps
ItersRangePoint
9
8.465625442272063e+58
8.825425083170634e+65
7.237313823686639e+64
7
-6.207156945681686e-303
-1.2633929192945347e-304
-1.7838017938976764e-303
8
-1.2071302776277865e+123
-1.7053146236540368e+120
-3.273288719661283e+120

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
15128
25128

end0.0ms

sample1.2s

Algorithm
intervals
Results
247.0ms1080×body2560valid
227.0ms5783×body80valid
174.0ms928×body1280valid
113.0ms2980×body80nan
70.0ms450×body640valid
29.0ms105×body5120valid
28.0ms258×body320valid
9.0ms123×body160valid