Details

Time bar (total: 15.0s)

sample17.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
2.0ms95×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06162
18162
done8162

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
18.0ms
(sqrt (+ x 1.0))
13.0ms
(+ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series288.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
67.0ms
(+ 1.0 (sqrt (+ x 1.0)))
190.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
80 → 80
Iterations

Useful iterations: done (1.2s)

IterNodesCost
014323232
133318532
2154117826
done500217636

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* flip3-+ div-exp prod-exp associate-/r/ sqrt-prod flip-+ log1p-expm1-u
3×fma-def associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative hypot-def pow-flip inv-pow
Counts
4 → 118
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
12.0ms
(+ 1.0 (sqrt (+ x 1.0)))
45.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
76.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series492.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(sqrt (+ x 1.0))
53.0ms
(+ 1.0 (sqrt (+ x 1.0)))
146.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
243.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.0s

Counts
130 → 130
Iterations

Useful iterations: done (2.0s)

IterNodesCost
019138446
148728682
2251426599
done500026280

prune530.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0))))
0.1b
(* (* x x) x)
0.1b
(* (* x x) x)
7.6b
(fma (/ (/ (* x x) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) -1/2 (fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
42×pow1
14×add-cbrt-cube add-exp-log
12×pow-plus pow-prod-up
8×add-sqr-sqrt
6×*-un-lft-identity associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
4×pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
2×associate-*l* pow3 *-commutative fma-udef unswap-sqr
Counts
4 → 80
Calls
4 calls:
0.0ms
(fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0))))
29.0ms
(* (* x x) x)
15.0ms
(* (* x x) x)
0.0ms
(fma (/ (/ (* x x) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) -1/2 (fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
941.0ms
(fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0))))
63.0ms
(* (* x x) x)
65.0ms
(* (* x x) x)
524.0ms
(fma (/ (/ (* x x) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) -1/2 (fma (/ 1/4 (* (+ (sqrt 1.0) 1.0) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0)))) (/ (* (* x x) x) 1.0) (fma (/ (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) (* (+ (sqrt 1.0) 1.0) (+ (sqrt 1.0) 1.0))) 1/8 (/ x (+ (sqrt 1.0) 1.0)))))

simplify1.7s

Counts
92 → 92
Iterations

Useful iterations: done (1.7s)

IterNodesCost
09028571
122422783
2153221909
done500020804

prune515.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
39×sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u associate-/r* flip3-+ associate-/r/ flip-+ log1p-expm1-u
3×fma-def
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative hypot-def
Counts
4 → 144
Calls
4 calls:
12.0ms
(sqrt (+ x 1.0))
26.0ms
(+ 1.0 (sqrt (+ x 1.0)))
27.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
78.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ x 1.0))
53.0ms
(+ 1.0 (sqrt (+ x 1.0)))
427.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
180.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.8s

Counts
156 → 156
Iterations

Useful iterations: done (3.8s)

IterNodesCost
022154719
157245706
2397442689
done500142201

prune634.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08203
113203
done13203

end0.0ms

sample561.0ms

Algorithm
intervals
Results
315.0ms7998×body80valid
66.0ms2729×body80nan
0.0ms2×body1280valid