Details

Time bar (total: 13.9s)

sample16.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
2.0ms95×body80nan

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))))

rewrite66.0ms

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:
12.0ms
(sqrt (+ x 1.0))
25.0ms
(+ 1.0 (sqrt (+ x 1.0)))
26.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series321.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
59.0ms
(+ 1.0 (sqrt (+ x 1.0)))
226.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify858.0ms

Counts
80 → 80
Iterations
IterNodes
done5002
21541
1333
0143

prune427.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
35×add-sqr-sqrt
26×times-frac
25×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
10×distribute-lft-out
8×pow1 sqrt-prod
7×fma-def
6×add-log-exp
4×expm1-log1p-u associate-/r* flip3-+ div-exp prod-exp associate-/r/ flip-+ log1p-expm1-u
3×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 → 122
Calls
4 calls:
13.0ms
(sqrt (+ 1.0 x))
46.0ms
(+ (sqrt (+ 1.0 x)) 1.0)
43.0ms
(/ 1 (+ (sqrt (+ 1.0 x)) 1.0))
82.0ms
(* x (/ 1 (+ (sqrt (+ 1.0 x)) 1.0)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ 1.0 x))
64.0ms
(+ (sqrt (+ 1.0 x)) 1.0)
156.0ms
(/ 1 (+ (sqrt (+ 1.0 x)) 1.0))
183.0ms
(* x (/ 1 (+ (sqrt (+ 1.0 x)) 1.0)))

simplify1.3s

Counts
134 → 134
Iterations
IterNodes
done5002
22533
1489
0191

prune561.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (+ 1.0 x)) 3)
0.2b
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
3.7b
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
6.8b
(/ x (+ (pow (sqrt (+ 1.0 x)) 3) (pow 1.0 3)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
43×add-sqr-sqrt
34×sqrt-prod
31×add-cube-cbrt
28×distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
14×sqrt-div
11×swap-sqr
9×associate-/r* sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log
8×flip3-+ flip-+
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u frac-times sum-cubes log1p-expm1-u unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-*l/ associate-*r/ associate-/r/
1×pow2 cube-mult pow-to-exp cbrt-undiv clear-num sub-neg rem-square-sqrt frac-2neg pow-plus flip3-- distribute-rgt-out-- fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp *-commutative cbrt-unprod div-inv sqrt-pow2 flip-- rem-cube-cbrt sqr-pow
Counts
4 → 174
Calls
4 calls:
8.0ms
(pow (sqrt (+ 1.0 x)) 3)
49.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
13.0ms
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
130.0ms
(/ x (+ (pow (sqrt (+ 1.0 x)) 3) (pow 1.0 3)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow (sqrt (+ 1.0 x)) 3)
19.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
90.0ms
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
257.0ms
(/ x (+ (pow (sqrt (+ 1.0 x)) 3) (pow 1.0 3)))

simplify3.5s

Counts
186 → 186
Iterations
IterNodes
done5000
24670
1743
0267

prune770.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3))) (+ (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))))
0.2b
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
3.7b
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
6.8b
(/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3)))

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
54×add-sqr-sqrt
44×*-un-lft-identity
38×frac-times
34×flip3-+ flip-+
32×frac-add
30×add-cube-cbrt
28×associate-*r/
26×sqrt-prod
25×times-frac associate-*l*
21×pow1
17×flip3-- flip--
13×add-cbrt-cube add-exp-log
11×swap-sqr associate-*l/
10×associate-*r*
8×sqrt-pow1 pow1/2
7×pow3 sum-cubes
6×distribute-lft-out add-log-exp unswap-sqr
5×pow-prod-up
4×expm1-log1p-u associate-/r* pow-prod-down associate-/r/ log1p-expm1-u
3×prod-exp pow-sqr cbrt-unprod associate-/l*
2×cbrt-undiv div-exp *-commutative div-inv
1×pow2 distribute-rgt-in clear-num sub-neg rem-square-sqrt frac-2neg distribute-lft-in pow-plus distribute-rgt-out-- fma-neg sqrt-unprod diff-log prod-diff
Counts
4 → 193
Calls
4 calls:
276.0ms
(* (/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3))) (+ (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))))
60.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
14.0ms
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
49.0ms
(/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3)))

series969.0ms

Counts
4 → 12
Calls
4 calls:
576.0ms
(* (/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3))) (+ (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))))
23.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
84.0ms
(- (* 1.0 1.0) (* (sqrt (+ 1.0 x)) 1.0))
286.0ms
(/ x (+ (* (+ 1.0 x) (sqrt (+ 1.0 x))) (pow 1.0 3)))

simplify988.0ms

Counts
205 → 205
Iterations
IterNodes
done5001
11734
0432

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
08

end0.0ms

sample848.0ms

Algorithm
intervals
Results
602.0ms7998×body80valid
88.0ms2729×body80nan
0.0ms2×body1280valid