Details

Time bar (total: 19.6s)

sample70.0ms

Algorithm
intervals
Results
32.0ms266×body80valid
8.0ms79×body80nan

simplify269.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize176.0ms

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)))

rewrite84.0ms

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))
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
115.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts
152 → 152
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01816137
14044128
211473279
348422634
done50002634

prune672.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-log-exp
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-diff
2×flip3-- sqrt-div flip--
1×sub-neg fma-neg diff-log difference-of-squares
Counts
4 → 66
Calls
4 calls:
45.0ms
(- (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))) b)
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
3.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (* (sqrt (sqrt (fma b b (- (* (* 4.0 a) c))))) (sqrt (sqrt (fma b b (- (* (* 4.0 a) c)))))) b)
99.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
134.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
78 → 78
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01201483
12721013
2750962
32728954
done5000943

prune539.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize117.0ms

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)))

rewrite45.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* b -2)))
11.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* (* 4.0 a) c))
115.0ms
(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* b -2)))
39.0ms
(/ (* a c) b)
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
91 → 91
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01611254
13671192
213241043
done50001029

prune618.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize165.0ms

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)))

rewrite102.0ms

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:
12.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
20.0ms
(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* b -2)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
189.0ms
(/ (* 2.0 c) (fma (* (/ a (sqrt b)) (/ c (sqrt b))) 2.0 (* b -2)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
143 → 143
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02642274
17032149
224881738
done50001732

prune986.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

regimes298.0ms

Accuracy

93.4% (1.0b remaining)

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

bsearch370.0ms

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

simplify20.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
069179
184177
297177
398177
done98177

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s8712×body80valid
319.0ms2994×body80nan