Details

Time bar (total: 12.8s)

sample33.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
6.0ms97×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

localize11.0ms

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))))

rewrite46.0ms

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-+ insert-posit16 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 → 74
Calls
3 calls:
5.0ms
(sqrt (+ x 1.0))
17.0ms
(+ 1.0 (sqrt (+ x 1.0)))
23.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series246.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
53.0ms
(+ 1.0 (sqrt (+ x 1.0)))
159.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts
83 → 83
Iterations
IterNodes
done5000
21180
1336
0146

prune303.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
18×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
8×sqrt-prod
7×fma-def distribute-lft-out
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 associate-/r*
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 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 → 78
Calls
3 calls:
5.0ms
(sqrt (+ x 1.0))
37.0ms
(+ (sqrt (+ x 1.0)) 1.0)
35.0ms
(/ x (+ (sqrt (+ x 1.0)) 1.0))

series317.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) 1.0)
207.0ms
(/ x (+ (sqrt (+ x 1.0)) 1.0))

simplify1.2s

Counts
87 → 87
Iterations
IterNodes
done5006
21161
1335
0146

prune317.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

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-+ insert-posit16 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 → 126
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
33.0ms
(+ (sqrt (+ x 1.0)) 1.0)
78.0ms
(* x (/ 1 (+ (sqrt (+ x 1.0)) 1.0)))
40.0ms
(/ 1 (+ (sqrt (+ x 1.0)) 1.0))

series425.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ x 1.0))
59.0ms
(+ (sqrt (+ x 1.0)) 1.0)
188.0ms
(* x (/ 1 (+ (sqrt (+ x 1.0)) 1.0)))
134.0ms
(/ 1 (+ (sqrt (+ x 1.0)) 1.0))

simplify1.5s

Counts
138 → 138
Iterations
IterNodes
done5001
21600
1480
0195

prune467.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0)))))
0.1b
(* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))))
0.1b
(* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0)))
6.8b
(fma -1/2 (/ (/ (* x x) (sqrt 1.0)) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0))))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
114×add-cbrt-cube add-exp-log
50×prod-exp cbrt-unprod
40×associate-*l*
39×add-sqr-sqrt
35×cbrt-undiv div-exp
32×times-frac
31×*-un-lft-identity
20×associate-*r*
19×add-cube-cbrt
18×associate-/r/
13×flip3-+ flip-+
10×frac-times
8×pow1
6×distribute-rgt-out associate-*l/ associate-*r/ unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×distribute-lft1-in sqrt-prod distribute-lft-out
2×pow-prod-down *-commutative fma-udef
1×cube-unmult
Counts
4 → 169
Calls
4 calls:
0.0ms
(fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0)))))
76.0ms
(* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))))
114.0ms
(* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0)))
1.0ms
(fma -1/2 (/ (/ (* x x) (sqrt 1.0)) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
802.0ms
(fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0)))))
160.0ms
(* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))))
216.0ms
(* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0)))
540.0ms
(fma -1/2 (/ (/ (* x x) (sqrt 1.0)) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (fma (* (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0)))) (/ x (* (sqrt 1.0) 1.0))) 1/8 (fma (/ 1/4 1.0) (* (/ x (+ 1.0 (sqrt 1.0))) (/ (* x x) (* (+ 1.0 (sqrt 1.0)) (+ 1.0 (sqrt 1.0))))) (/ x (+ 1.0 (sqrt 1.0))))))

simplify2.3s

Counts
181 → 181
Iterations
IterNodes
done5001
24537
1982
0311

prune910.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes35.0ms

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

sample890.0ms

Algorithm
intervals
Results
526.0ms7996×body80valid
186.0ms2742×body80nan
28.0ms4×body1280valid