Details

Time bar (total: 8.0s)

sample44.0ms

Algorithm
intervals
Results
8.0ms26×body1280valid
7.0ms192×body80valid
7.0ms33×body2560valid
4.0ms113×body80nan
1.0ms10×body640valid
1.0ms4×body5120valid
1.0ms9×body320valid
0.0ms7×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.4b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
1094×add-sqr-sqrt
580×prod-diff
482×*-un-lft-identity
330×add-cube-cbrt
318×associate-*r*
307×unswap-sqr
256×sqrt-prod
231×associate-*l*
208×difference-of-squares
105×swap-sqr
97×*-commutative
92×distribute-rgt-neg-in
84×times-frac
78×distribute-lft-neg-in
76×distribute-lft-out--
26×neg-mul-1
25×fma-neg
12×associate-/r*
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv associate--l- neg-sub0 sub-neg sqrt-div div-sub div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 817
Calls
4 calls:
63.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
35.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
90.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify205.0ms

Algorithm
egg-herbie
Counts
829 → 829
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0193220316
1500115481

prune713.0ms

Filtered
829 candidates to 206 candidates (75.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New8209829
Fresh000
Picked101
Done000
Total8219830

Merged error: 5.1b

Counts
830 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
1474×add-sqr-sqrt
822×*-un-lft-identity
606×times-frac
580×prod-diff
524×add-cube-cbrt
381×associate-*r*
328×unswap-sqr
295×associate-*l*
292×sqrt-prod
280×difference-of-squares
148×distribute-lft-out--
128×distribute-rgt-neg-in
118×*-commutative
105×swap-sqr
97×associate-/r*
78×distribute-lft-neg-in
30×associate-/r/
26×neg-mul-1
25×add-exp-log fma-neg
17×associate-/l*
13×add-cbrt-cube
12×div-exp
10×add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp clear-num remove-double-div
2×sub-neg frac-2neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log cbrt-unprod inv-pow
Counts
4 → 1108
Calls
4 calls:
61.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
36.0ms
(- (* b b) (* 4.0 (* a c)))
46.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
53.0ms
(- (* b b) (* 4.0 (* a c)))
86.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify268.0ms

Algorithm
egg-herbie
Counts
1120 → 1120
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0255925667
1500121115

prune1.5s

Filtered
1120 candidates to 347 candidates (69.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New111641120
Fresh448
Picked011
Done000
Total112091129

Merged error: 5.1b

Counts
1129 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
1017×add-sqr-sqrt
580×prod-diff
421×*-un-lft-identity
305×add-cube-cbrt
299×unswap-sqr
294×associate-*r*
247×sqrt-prod
207×associate-*l*
190×difference-of-squares
105×swap-sqr
89×*-commutative
83×distribute-rgt-neg-in
78×distribute-lft-neg-in
58×distribute-lft-out--
26×neg-mul-1
25×fma-neg
21×times-frac
10×add-log-exp
7×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×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 743
Calls
4 calls:
58.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
35.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
48.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify187.0ms

Algorithm
egg-herbie
Counts
755 → 755
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0165218955
1500113833

prune575.0ms

Filtered
755 candidates to 170 candidates (77.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New7541755
Fresh167
Picked011
Done011
Total7559764

Merged error: 5.1b

Counts
764 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
697×add-sqr-sqrt
287×sqrt-prod
250×prod-diff
234×unswap-sqr
213×*-un-lft-identity
197×difference-of-squares
105×add-cube-cbrt
79×distribute-rgt-neg-in
78×distribute-lft-neg-in
54×distribute-lft-out--
52×associate-*l*
39×swap-sqr *-commutative
26×neg-mul-1
10×fma-neg
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 388
Calls
4 calls:
46.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
49.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
48.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify143.0ms

Algorithm
egg-herbie
Counts
400 → 400
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
069011846
118669382
250019159

prune596.0ms

Filtered
400 candidates to 119 candidates (70.3%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New4000400
Fresh066
Picked011
Done022
Total4009409

Merged error: 5.1b

Counts
409 → 9

regimes201.0ms

Accuracy

85.3% (4.2b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 34.3b

bsearch65.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
9
-2.816841330355383e-75
-7.368877589091801e-81
-1.0996442222619662e-75

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03616
13616

end0.0ms

sample1.1s

Algorithm
intervals
Results
253.0ms1103×body2560valid
233.0ms5872×body80valid
170.0ms890×body1280valid
99.0ms2796×body80nan
66.0ms453×body640valid
28.0ms102×body5120valid
27.0ms231×body320valid
8.0ms116×body160valid