Details

Time bar (total: 18.1s)

sample57.0ms

Algorithm
intervals
Results
22.0ms286×body80valid
15.0ms79×body80nan

simplify193.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize151.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
137.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
177 → 177
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02086992
15084619
226703571
done50013570

prune666.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.7b

localize148.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
21.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
95 → 95
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01782699
14522598
219502248
done50012216

prune739.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize143.0ms

Local error

Found 4 expressions with local error:

22.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
1.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))

series598.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
166.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))

simplify2.6s

Counts
67 → 67
Iterations

Useful iterations: 3 (979.0ms)

IterNodesCost
0881442
12051264
27021121
337241103
done50001103

prune631.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

localize142.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.6b
(/ (* a c) b)
4.6b
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
6×times-frac fma-neg associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×flip3-- frac-2neg sqrt-div prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 104
Calls
4 calls:
59.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(/ (* a c) b)
10.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
32.0ms
(/ (* a c) b)
112.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
116 → 116
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01992109
15171828
228481539
done50001465

prune634.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

regimes205.0ms

Accuracy

88.8% (1.5b remaining)

Error of 7.4b against oracle of 5.9b and baseline of 19.4b

bsearch323.0ms

Steps
ItersRangePoint
8
3932480935863.943
2020002846347102.2
929319867835151.5
9
-7.561250615295736e+156
-1.350243324689865e+150
-4.919628179067154e+153

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043120
148120
done48120

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s8765×body80valid
388.0ms2894×body80nan