Details

Time bar (total: 9.1s)

sample39.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
4.0ms102×body80nan

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

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:
33.0ms
(+ 1.0 (sqrt (+ 1.0 x)))
13.0ms
(sqrt (+ 1.0 x))
51.0ms
(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series341.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ 1.0 (sqrt (+ 1.0 x)))
54.0ms
(sqrt (+ 1.0 x))
228.0ms
(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify865.0ms

Counts
80 → 80
Iterations
IterNodes
done5000
21548
1335
0143

prune352.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (pow (+ 1.0 x) 1/2))
0.0b
(pow (+ 1.0 x) 1/2)
0.2b
(/ x (+ 1.0 (pow (+ 1.0 x) 1/2)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
12×times-frac
6×add-exp-log distribute-lft-out
5×add-cbrt-cube add-log-exp
4×pow1 associate-/r* unpow-prod-down
3×expm1-log1p-u pow-unpow fma-def log1p-expm1-u associate-/l*
2×flip3-+ associate-/r/ flip-+
1×pow-to-exp cbrt-undiv +-commutative clear-num sum-log pow-pow frac-2neg div-exp pow-exp div-inv unpow1/2 sqr-pow
Counts
3 → 73
Calls
3 calls:
24.0ms
(+ 1.0 (pow (+ 1.0 x) 1/2))
14.0ms
(pow (+ 1.0 x) 1/2)
83.0ms
(/ x (+ 1.0 (pow (+ 1.0 x) 1/2)))

series530.0ms

Counts
3 → 9
Calls
3 calls:
138.0ms
(+ 1.0 (pow (+ 1.0 x) 1/2))
112.0ms
(pow (+ 1.0 x) 1/2)
279.0ms
(/ x (+ 1.0 (pow (+ 1.0 x) 1/2)))

simplify1.3s

Counts
82 → 82
Iterations
IterNodes
done5001
22581
1540
0199

prune457.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

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)))
4.6b
(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
6.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×associate-/r* sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div 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 → 194
Calls
4 calls:
14.0ms
(pow (sqrt (+ 1.0 x)) 3)
33.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
42.0ms
(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
79.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(pow (sqrt (+ 1.0 x)) 3)
24.0ms
(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
69.0ms
(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
289.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

simplify530.0ms

Counts
206 → 206
Iterations
IterNodes
done5001
1950
0325

prune939.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ x (- (* 1.0 1.0) (+ 1.0 x))) (- 1.0 (pow (+ 1.0 x) 1/2)))
0.0b
(pow (+ 1.0 x) 1/2)
4.5b
(- (* 1.0 1.0) (+ 1.0 x))
4.6b
(- 1.0 (pow (+ 1.0 x) 1/2))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
85×*-un-lft-identity
78×add-sqr-sqrt
76×prod-diff
59×add-cube-cbrt
42×unpow-prod-down
26×distribute-rgt-in distribute-lft-in
18×associate-*l*
13×times-frac
12×sqr-pow
11×distribute-lft-out add-log-exp
10×add-exp-log difference-of-squares
9×add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg fma-neg log1p-expm1-u
3×pow-unpow diff-log
2×frac-times prod-exp associate-*r/ associate-/r/ cbrt-unprod distribute-lft-out-- unswap-sqr
1×pow-to-exp cbrt-undiv sum-log pow-pow div-exp pow-prod-down associate-*l/ pow-exp *-commutative div-inv associate--r+ unpow1/2
Counts
4 → 187
Calls
4 calls:
231.0ms
(* (/ x (- (* 1.0 1.0) (+ 1.0 x))) (- 1.0 (pow (+ 1.0 x) 1/2)))
8.0ms
(pow (+ 1.0 x) 1/2)
28.0ms
(- (* 1.0 1.0) (+ 1.0 x))
38.0ms
(- 1.0 (pow (+ 1.0 x) 1/2))

series493.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (/ x (- (* 1.0 1.0) (+ 1.0 x))) (- 1.0 (pow (+ 1.0 x) 1/2)))
135.0ms
(pow (+ 1.0 x) 1/2)
22.0ms
(- (* 1.0 1.0) (+ 1.0 x))
175.0ms
(- 1.0 (pow (+ 1.0 x) 1/2))

simplify503.0ms

Counts
199 → 199
Iterations
IterNodes
done5001
11030
0339

prune730.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done9
19
07

end0.0ms

sample674.0ms

Algorithm
intervals
Results
340.0ms7997×body80valid
107.0ms2708×body80nan
1.0ms3×body1280valid