Details

Time bar (total: 14.3s)

sample19.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms95×body80nan

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
done8
18
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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))))

rewrite79.0ms

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))
19.0ms
(+ 1.0 (sqrt (+ x 1.0)))
47.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series320.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
73.0ms
(+ 1.0 (sqrt (+ x 1.0)))
212.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
80 → 80
Iterations
IterNodes
done5002
21541
1333
0143

prune396.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* flip3-+ div-exp prod-exp associate-/r/ sqrt-prod flip-+ log1p-expm1-u
3×fma-def 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 → 118
Calls
4 calls:
11.0ms
(sqrt (+ x 1.0))
18.0ms
(+ 1.0 (sqrt (+ x 1.0)))
26.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
108.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (+ x 1.0))
76.0ms
(+ 1.0 (sqrt (+ x 1.0)))
134.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
200.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.7s

Counts
130 → 130
Iterations
IterNodes
done5000
22514
1487
0191

prune612.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize53.0ms

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)))
3.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite262.0ms

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 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 → 170
Calls
4 calls:
159.0ms
(* (/ 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))))))
45.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
43.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0ms
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series951.0ms

Counts
4 → 12
Calls
4 calls:
570.0ms
(* (/ 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))))))
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
74.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
285.0ms
(/ x (fma (* 1.0 1.0) 1.0 (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify1.7s

Counts
182 → 182
Iterations
IterNodes
done5001
11153
0367

prune900.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
39×sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u associate-/r* flip3-+ associate-/r/ flip-+ log1p-expm1-u
3×fma-def
2×cbrt-undiv sqrt-div div-exp prod-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/ *-commutative hypot-def
Counts
4 → 144
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
20.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
80.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series734.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
76.0ms
(+ 1.0 (sqrt (+ x 1.0)))
397.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
211.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.1s

Counts
156 → 156
Iterations
IterNodes
done5001
23974
1572
0221

prune550.0ms

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

simplify3.0ms

Iterations
IterNodes
done13
113
08

end0.0ms

sample804.0ms

Algorithm
intervals
Results
435.0ms7998×body80valid
85.0ms2729×body80nan
0.0ms2×body1280valid