Details

Time bar (total: 10.6s)

sample43.0ms

Algorithm
intervals
Results
20.0ms129×pre10240exit
8.0ms256×body80valid
3.0ms127×pre80true

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1107
2127
done127

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.8b
(/ x0 (- 1.0 x1))
7.6b
(- (/ x0 (- 1.0 x1)) x0)

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
103×*-un-lft-identity
76×times-frac
69×add-cube-cbrt
63×prod-diff
21×fma-neg
18×difference-of-squares
17×distribute-lft-out--
10×associate-/r/
6×flip3-- flip--
5×associate-/r* div-inv
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num
Counts
2 → 140
Calls
2 calls:
21.0ms
(/ x0 (- 1.0 x1))
109.0ms
(- (/ x0 (- 1.0 x1)) x0)

series101.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(/ x0 (- 1.0 x1))
57.0ms
(- (/ x0 (- 1.0 x1)) x0)

simplify2.2s

Counts
146 → 146
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01902805
14222150
29511818
331411524
done50011501

prune173.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (cbrt x0) (- 1.0 x1))
6.4b
(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt *-un-lft-identity
30×times-frac
21×add-cube-cbrt
18×cbrt-prod
7×distribute-lft-out-- difference-of-squares
6×associate-/l*
5×associate-/r*
4×add-exp-log
3×add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv
Counts
2 → 67
Calls
2 calls:
26.0ms
(/ (cbrt x0) (- 1.0 x1))
1.0ms
(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

series251.0ms

Counts
2 → 6
Calls
2 calls:
104.0ms
(/ (cbrt x0) (- 1.0 x1))
147.0ms
(fma (/ (* (cbrt x0) (cbrt x0)) 1) (/ (cbrt x0) (- 1.0 x1)) (- x0))

simplify1.8s

Counts
73 → 73
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01511049
1308968
2874878
33337847
done5000811

prune182.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
6.9b
(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
57×*-un-lft-identity
54×times-frac
42×sqrt-prod
30×cbrt-prod
29×add-cube-cbrt
28×difference-of-squares
14×distribute-lft-out--
9×associate-/r*
6×associate-/l*
4×add-exp-log
3×add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv
Counts
2 → 95
Calls
2 calls:
26.0ms
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
0.0ms
(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series612.0ms

Counts
2 → 6
Calls
2 calls:
311.0ms
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
301.0ms
(fma (/ (* (cbrt x0) (cbrt x0)) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify914.0ms

Counts
101 → 101
Iterations

Useful iterations: done (910.0ms)

IterNodesCost
02212097
15161968
216371820
done50011763

prune207.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
0.5b
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
0.7b
(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
6.9b
(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
93×add-sqr-sqrt
65×*-un-lft-identity
54×times-frac
42×cbrt-prod sqrt-prod
37×add-cube-cbrt
28×difference-of-squares
14×distribute-lft-out--
9×associate-/r*
7×add-exp-log
6×unpow-prod-down cube-prod add-cbrt-cube associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult unpow3 associate-/r/ sqr-pow
1×cbrt-undiv pow-to-exp flip3-- pow-pow frac-2neg pow1/3 div-exp pow-exp clear-num flip-- rem-cbrt-cube fma-udef div-inv rem-cube-cbrt
Counts
4 → 143
Calls
4 calls:
2.0ms
(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
25.0ms
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
3.0ms
(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
0.0ms
(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

series951.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(cbrt (pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3))
242.0ms
(/ (cbrt x0) (- (sqrt 1.0) (sqrt x1)))
291.0ms
(pow (fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0)) 3)
208.0ms
(fma (/ (pow x0 2/3) (+ (sqrt 1.0) (sqrt x1))) (/ (cbrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))

simplify1.1s

Counts
155 → 155
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02994115
17163690
223993355
done50003351

prune389.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 5.1b

regimes57.0ms

Accuracy

69.1% (0.6b remaining)

Error of 5.5b against oracle of 4.9b and baseline of 6.9b

bsearch20.0ms

Steps
ItersRangePoint
4
1.855
2.985
1.9944531249999997

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02651
12851
done2851

end0.0ms

sample1.2s

Algorithm
intervals
Results
753.0ms3974×pre10240exit
200.0ms8000×body80valid
78.0ms4026×pre80true