Details

Time bar (total: 6.3s)

sample284.0ms

Algorithm
intervals
Results
7.0ms209×body80valid
6.0ms34×body2560valid
4.0ms79×body80nan
3.0ms22×body1280valid
2.0ms18×body640valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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:
42.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune302.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
4.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.6b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
30.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
145.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify123.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
07613434
134903258
250023250

prune522.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
1.8b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.4b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 495
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
25.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
185.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
160.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015618691
150028044

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
853×times-frac
555×add-sqr-sqrt
554×*-un-lft-identity
382×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
61×prod-diff
41×div-inv
37×add-exp-log
29×div-exp
25×associate-/r*
21×distribute-lft-neg-in
16×add-cbrt-cube
13×associate-/l*
11×fma-neg
10×1-exp add-log-exp
8×cbrt-undiv
7×neg-mul-1
5×pow1
4×expm1-log1p-u rec-exp log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ associate-/l/
Counts
4 → 518
Calls
4 calls:
36.0ms
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
530 → 530
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
018269644
150028321

prune492.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.6b

regimes244.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.4b

bsearch132.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
1.0551401351209752e+102
7
1.991108345769127e-268
5.063898629501046e-267
9.658303386763521e-268
9
-2.3467190644739184e+107
-3.2019781887028674e+101
-1.7431685240570133e+102

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04022
14022

end0.0ms

sample971.0ms

Algorithm
intervals
Results
199.0ms1072×body2560valid
185.0ms5838×body80valid
132.0ms882×body1280valid
89.0ms2846×body80nan
70.0ms497×body640valid
23.0ms102×body5120valid
19.0ms220×body320valid
6.0ms105×body160valid