Details

Time bar (total: 18.0s)

sample56.0ms

Algorithm
intervals
Results
23.0ms276×body80valid
7.0ms92×body80nan

simplify258.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize152.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts
163 → 163
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
01796238
14174208
211683343
347922690
done50002690

prune717.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.0b

localize137.0ms

Local error

Found 4 expressions with local error:

7.2b
(+ (- 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)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
8×add-log-exp
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- distribute-rgt-neg-in sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 72
Calls
4 calls:
23.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
33.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series602.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
84 → 84
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01521636
13891532
213071322
done50001289

prune735.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize125.0ms

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)))

rewrite51.0ms

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:
19.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
180.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
159.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
95 → 95
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01782699
14272590
213452248
done50002205

prune824.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.0b

localize107.0ms

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) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×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
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 159
Calls
4 calls:
62.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* a c) b)
152.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms
(/ (* a c) b)
277.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
171 → 171
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02546404
16074427
219443461
done50012821

prune758.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes255.0ms

Accuracy

93.3% (0.9b remaining)

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

bsearch316.0ms

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
049138
161138
done61138

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8712×body80valid
592.0ms2914×body80nan