Details

Time bar (total: 9.2s)

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
3.0ms69×body80nan

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×add-sqr-sqrt
12×times-frac add-cube-cbrt
5×distribute-lft-out
4×associate-/r* add-cbrt-cube add-exp-log sqrt-prod
3×pow1 associate-/l*
2×expm1-log1p-u flip3-+ sqrt-div associate-/r/ flip-+ insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
2 → 56
Calls
2 calls:
5.0ms
(sqrt (+ x 1.0))
19.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series212.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(sqrt (+ x 1.0))
171.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify471.0ms

Counts
62 → 62
Iterations
IterNodes
done2021
21078
1305
0133

prune228.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
11.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series1.4s

Counts
4 → 12
Calls
4 calls:
565.0ms
(* (cbrt x) (cbrt x))
225.0ms
(cbrt x)
328.0ms
(cbrt x)
277.0ms
(cbrt x)

simplify647.0ms

Counts
97 → 97
Iterations
IterNodes
done2002
31106
2364
1141
067

prune357.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.1b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
45×add-sqr-sqrt
42×*-un-lft-identity
32×flip3-+ flip-+
30×associate-*r/
28×add-cube-cbrt
26×sqrt-prod
21×pow1
20×associate-*l*
19×times-frac
16×frac-sub
14×frac-times
13×add-cbrt-cube add-exp-log
11×swap-sqr
10×associate-*r*
9×associate-*l/
8×sqrt-pow1 pow1/2
6×distribute-lft-out add-log-exp unswap-sqr
5×pow-prod-up
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u sub-div
3×associate-/r* 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 flip3-- distribute-rgt-out-- fma-neg sqrt-unprod diff-log prod-diff flip--
Counts
4 → 174
Calls
4 calls:
190.0ms
(* (/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
34.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
22.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
4.0ms
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series889.0ms

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
28.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
87.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
284.0ms
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify831.0ms

Counts
186 → 186
Iterations
IterNodes
done2002
11148
0371

prune815.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
284×*-un-lft-identity
190×sqrt-prod
187×add-sqr-sqrt
184×add-cube-cbrt
50×distribute-lft-out
34×associate-/r*
10×add-cbrt-cube add-exp-log associate-/l*
9×div-inv
4×pow1 cbrt-undiv div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg flip3-+ sqrt-div flip-+ associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
Counts
3 → 291
Calls
3 calls:
5.0ms
(sqrt (+ x 1.0))
31.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
30.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series323.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
150.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
140.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify797.0ms

Counts
300 → 300
Iterations
IterNodes
done2002
1982
0372

prune803.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes58.0ms

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
done8
18
06

end0.0ms

sample824.0ms

Algorithm
intervals
Results
496.0ms7998×body80valid
149.0ms2598×body80nan
0.0ms2×body1280valid