Details

Time bar (total: 12.3s)

sample102.0ms

Algorithm
intervals
Results
27.0ms188×body80valid
18.0ms36×body2560valid
9.0ms24×body1280valid
8.0ms108×body80nan
5.0ms17×body640valid
3.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
410216
511116
done11116

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
108.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
12.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
80.0ms
(- (* b b) (* 4.0 (* a c)))
128.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01521592
14031496
215981332
done50001326

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 118
Calls
4 calls:
92.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
17.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
68.0ms
(- (* b b) (* 4.0 (* a c)))
120.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
130 → 130
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02183137
15672809
226312613
done50002611

prune396.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
13×add-cbrt-cube
12×*-un-lft-identity
10×prod-exp
8×add-cube-cbrt add-log-exp
7×pow1 associate-*l*
6×associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg div-exp cbrt-unprod difference-of-squares
3×times-frac
2×cbrt-undiv distribute-rgt-in frac-times rec-exp distribute-lft-in sqrt-div diff-log 1-exp associate-*r/ distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
207.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms
(- (* b b) (* 4.0 (* a c)))
85.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
63.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
96 → 96
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01691924
14851781
224991509
done50001503

prune307.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.1b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.1b

regimes215.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.8b

bsearch212.0ms

Steps
ItersRangePoint
9
4.939518845348872e-48
4.7173742985844417e-39
1.4070882317677973e-46
10
-2.8734245235493903e+48
-2.602501271628617e+37
-2.8472042802820317e+48

simplify32.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s5856×body80valid
660.0ms1074×body2560valid
436.0ms223×body320valid
416.0ms903×body1280valid
308.0ms2902×body80nan
130.0ms451×body640valid
59.0ms112×body5120valid
16.0ms111×body160valid