Details

Time bar (total: 17.6s)

sample59.0ms

Algorithm
intervals
Results
23.0ms276×body80valid
7.0ms92×body80nan

simplify247.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize127.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

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:
47.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
177 → 177
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune638.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.0b

localize168.0ms

Local error

Found 4 expressions with local error:

7.2b
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×prod-diff sqrt-prod
2×pow1/3 sqrt-div
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log
Counts
4 → 65
Calls
4 calls:
39.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
157.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
162.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts
77 → 77
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01641691
13901578
211211356
340391320
done50001319

prune606.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize128.0ms

Local error

Found 4 expressions with local error:

8.8b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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:
17.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
137.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
150.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
123.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
95 → 95
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01782699
14272590
213452248
done50002205

prune728.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b
(/ (* a c) b)
4.8b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
59×add-sqr-sqrt
58×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 159
Calls
4 calls:
67.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ (* a c) b)
172.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms
(/ (* a c) b)
140.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
171 → 171
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02616392
16094415
219553464
done50012822

prune814.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes277.0ms

Accuracy

93.3% (0.9b remaining)

Error of 7.2b against oracle of 6.3b and baseline of 20.0b

bsearch255.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
4.623731436085777e+144
7
-6.338089291324522e+142
-9.408663701389454e+140
-2.415824536209925e+141

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
049135
158135
done58135

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s8712×body80valid
718.0ms2914×body80nan