Details

Time bar (total: 3.8s)

sample44.0ms

Algorithm
intervals
Results
10.0ms45×body2560valid
7.0ms170×body80valid
6.0ms31×body1280valid
4.0ms99×body80nan
2.0ms11×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms5×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.4b

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))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
20.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune318.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1609169
Fresh000
Picked101
Done000
Total1619170

Merged error: 6.2b

Counts
170 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
16.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06563422
125942238
250012193

prune289.0ms

Filtered
177 candidates to 90 candidates (50.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1752177
Fresh358
Picked011
Done000
Total1788186

Merged error: 6.2b

Counts
186 → 8

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune17.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done011
Total088

Merged error: 6.2b

Counts
8 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt b)
0.8b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-prod sqrt-prod
2×flip3-- sqrt-div flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg pow1/3 diff-log prod-diff fma-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt b)
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
1.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt b)
49.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
136.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))

simplify101.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0246491
1810444
23581426
35001423

prune204.0ms

Filtered
68 candidates to 59 candidates (86.8%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New67168
Fresh055
Picked011
Done022
Total67976

Merged error: 6.2b

Counts
76 → 9

regimes239.0ms

Accuracy

83.6% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 33.3b

bsearch112.0ms

Steps
ItersRangePoint
8
3.6696373663460875e+72
1.716395662560696e+75
3.7662531131329464e+74
10
-1.343161105949918e-105
-1.3714095314265258e-117
-1.2029085178736339e-108

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.1s

Algorithm
intervals
Results
233.0ms5952×body80valid
231.0ms1018×body2560valid
165.0ms886×body1280valid
107.0ms2961×body80nan
66.0ms446×body640valid
32.0ms115×body5120valid
25.0ms221×body320valid
8.0ms105×body160valid