Details

Time bar (total: 17.9s)

sample82.0ms

Algorithm
intervals
Results
38.0ms276×body80valid
18.0ms92×body80nan

simplify207.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

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

localize131.0ms

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)))

rewrite151.0ms

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:
60.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.5s

Counts
163 → 163
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01796238
14174208
211683343
347922690
done50002690

prune628.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.0b

localize133.0ms

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)))

rewrite64.0ms

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:
18.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series499.0ms

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))))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
140.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
152.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
84 → 84
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01521636
13891532
213071322
done50001289

prune747.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize187.0ms

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)))

rewrite65.0ms

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:
15.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
137.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
95 → 95
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01782699
14272590
213452248
done50002205

prune848.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.0b

localize180.0ms

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) (fma 2.0 (/ (* a c) b) (* -2 b)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-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×add-log-exp
7×neg-mul-1
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num 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 pow1/2 neg-log
Counts
4 → 153
Calls
4 calls:
52.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(/ (* a c) b)
10.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(/ (* a c) b)
118.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
165 → 165
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02506245
15734278
217803356
done50002715

prune767.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes264.0ms

Accuracy

93.3% (0.9b remaining)

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

bsearch326.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
1.0250863020074382e+144
7
-6.338089291324522e+142
-9.408663701389454e+140
-2.415824536209925e+141

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
046131
157131
done57131

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s8712×body80valid
361.0ms2914×body80nan