Details

Time bar (total: 21.0s)

sample69.0ms

Algorithm
intervals
Results
36.0ms266×body80valid
6.0ms79×body80nan

simplify244.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize142.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×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
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* b b) (* (* 4.0 a) c))
143.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.3s

Counts
152 → 152
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01816137
14044128
211473279
348422634
done50002634

prune661.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize128.0ms

Local error

Found 4 expressions with local error:

9.7b
(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
20.1b
(sqrt (fma b b (- (* (* 4.0 a) c))))
20.1b
(sqrt (fma b b (- (* (* 4.0 a) c))))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2
2×sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-- flip3-+ neg-log flip-- flip-+
Counts
4 → 72
Calls
4 calls:
26.0ms
(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
4.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(+ (- b) (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))))
117.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
137.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts
84 → 84
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01061400
1265967
2868909
33099897
done5000895

prune731.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize129.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.4b
(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* b -2)))
6.0b
(/ (* a c) b)
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 79
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* b -2)))
19.0ms
(/ (* a c) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* b -2)))
29.0ms
(/ (* a c) b)
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
91 → 91
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01611254
13671192
213241043
done50001029

prune626.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize113.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.7b
(* (/ a (sqrt b)) (/ c (sqrt b)))
1.0b
(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* b -2)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
51×times-frac
33×add-cube-cbrt *-un-lft-identity
27×sqrt-prod
22×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp add-log-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* div-inv
2×flip3-- sqrt-div flip--
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 131
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
14.0ms
(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* b -2)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
142.0ms
(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* b -2)))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
143 → 143
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02642274
17032149
224881738
done50001732

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

regimes325.0ms

Accuracy

93.4% (1.0b remaining)

Error of 7.5b against oracle of 6.6b and baseline of 21.1b

bsearch460.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.2875942964765074e+78
10
-3.579862835853504e-259
-1.0472779812871276e-269
-4.452231346955638e-267
9
-4.4874797001979404e+160
-1.588602326591779e+153
-1.3506760573432116e+154

simplify13.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
057177
172175
283175
done83175

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8712×body80valid
291.0ms2994×body80nan