Details

Time bar (total: 12.8s)

sample27.0ms

Algorithm
intervals
Results
12.0ms255×body80valid
7.0ms82×body80nan
0.0ms1×body1280valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune3.0ms

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))))

rewrite41.0ms

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:
9.0ms
(sqrt (+ x 1.0))
31.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series241.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(sqrt (+ x 1.0))
189.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
62 → 62
Iterations
IterNodes
done5000
21078
1305
0133

prune228.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
32×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out
7×pow1
4×associate-/r* div-exp prod-exp associate-/r/ sqrt-prod
3×expm1-log1p-u flip3-+ associate-*l* flip-+ insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative hypot-def pow-flip inv-pow
Counts
3 → 104
Calls
3 calls:
5.0ms
(sqrt (+ x 1.0))
29.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
60.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series367.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(sqrt (+ x 1.0))
131.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
199.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.0s

Counts
113 → 113
Iterations
IterNodes
done5014
21636
1448
0182

prune375.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
0.1b
(* x (/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))))
1.6b
(expm1 (log1p (sqrt (+ x 1.0))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
33×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
8×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* div-exp prod-exp associate-/r/ sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×rem-sqrt-square expm1-log1p clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative hypot-def pow-flip inv-pow expm1-udef
Counts
4 → 116
Calls
4 calls:
9.0ms
(sqrt (+ x 1.0))
15.0ms
(/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
34.0ms
(* x (/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))))
0.0ms
(expm1 (log1p (sqrt (+ x 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
313.0ms
(/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
476.0ms
(* x (/ 1 (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))))
231.0ms
(expm1 (log1p (sqrt (+ x 1.0))))

simplify1.3s

Counts
128 → 128
Iterations
IterNodes
done5001
21494
1463
0194

prune460.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 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)))
2.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.5b
(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

rewrite232.0ms

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:
165.0ms
(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
40.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
20.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
4.0ms
(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
660.0ms
(* (/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
24.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
66.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
306.0ms
(/ x (fma (+ 1.0 x) (sqrt (+ 1.0 x)) (* (* 1.0 1.0) 1.0)))

simplify3.2s

Counts
186 → 186
Iterations
IterNodes
done5000
24791
11245
0396

prune946.0ms

Pruning

4 alts after pruning (1 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

simplify1.0ms

Iterations
IterNodes
done13
113
08

end0.0ms

sample676.0ms

Algorithm
intervals
Results
416.0ms7994×body80valid
121.0ms2721×body80nan
1.0ms6×body1280valid