Details

Time bar (total: 18.7s)

sample286.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
6.0ms197×body80valid
4.0ms27×body1280valid
3.0ms116×body80nan
2.0ms13×body640valid
1.0ms7×body320valid
0.0ms2×body5120valid
0.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
52.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05493055
118262150
250022063

prune365.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b
(- (* b_2 b_2) (* a c))
7.0b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
1339×times-frac
946×add-sqr-sqrt
940×*-un-lft-identity
926×add-cube-cbrt
749×prod-diff
323×sqrt-prod
210×distribute-rgt-neg-in
207×distribute-lft-neg-in
69×neg-mul-1
60×div-inv
35×fma-neg
8×add-log-exp
7×distribute-lft-out--
6×add-exp-log add-cbrt-cube associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num frac-sub sub-div
Counts
4 → 889
Calls
4 calls:
7.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
36.0ms
(- (* b_2 b_2) (* a c))
86.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify265.0ms

Algorithm
egg-herbie
Counts
901 → 901
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0195839816
1500125884

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b_2 b_2) (* a c))
0.3b
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
10.0b
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
73×times-frac
69×add-sqr-sqrt
56×*-un-lft-identity
54×add-cube-cbrt
35×fma-neg prod-diff
18×distribute-lft-neg-in distribute-rgt-neg-in
13×add-exp-log associate-*r*
10×sqrt-div
9×sqrt-prod add-cbrt-cube
8×add-log-exp
7×pow1 flip3-- flip--
6×neg-mul-1 associate-*l* frac-sub unswap-sqr
4×expm1-log1p-u frac-times associate-*l/ prod-exp log1p-expm1-u div-inv
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod sub-div
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp distribute-rgt-out-- sqrt-pow1 pow1/2 1-exp div-sub pow-prod-down *-commutative
Counts
4 → 173
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
36.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
100.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
84.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07522220
127481911
250021871

prune460.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
10.7b
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite578.0ms

Algorithm
rewrite-expression-head
Rules
6799×times-frac
3868×add-sqr-sqrt
3835×*-un-lft-identity
3818×add-cube-cbrt
2619×prod-diff
961×sqrt-prod
703×distribute-rgt-neg-in
702×distribute-lft-neg-in
247×associate-/r/
234×neg-mul-1
220×div-inv
214×sqrt-div
109×flip3-- flip--
35×fma-neg
24×associate-/r*
15×add-exp-log
14×difference-of-squares
9×add-cbrt-cube
8×add-log-exp
7×div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp diff-log 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 div-sub clear-num frac-sub inv-pow
Counts
4 → 2841
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
191.0ms
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
83.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
84.0ms
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Algorithm
egg-herbie
Counts
2853 → 2853
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05002169217

prune11.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

regimes267.0ms

Accuracy

83.5% (4.8b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 35.0b

bsearch181.0ms

Steps
ItersRangePoint
9
2.6683347110001497e+63
3.895668027475672e+69
1.5763246439716715e+69
9
-6.372026032033847e-139
-5.609109599303715e-148
-6.273278539774699e-139
10
-4.748004806532821e-81
-3.21055753719808e-93
-1.466065355378786e-87
8
-1.832018824537513e-72
-3.025657799658831e-77
-3.4003426496549383e-77

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03725
13725

end0.0ms

sample988.0ms

Algorithm
intervals
Results
205.0ms1048×body2560valid
186.0ms5813×body80valid
144.0ms930×body1280valid
88.0ms2899×body80nan
59.0ms471×body640valid
25.0ms110×body5120valid
23.0ms226×body320valid
7.0ms115×body160valid