Details

Time bar (total: 15.4s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
3.0ms89×body80nan

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06162
18162
done8162

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

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:
24.0ms
(+ 1.0 (sqrt (+ x 1.0)))
11.0ms
(sqrt (+ x 1.0))
45.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series340.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(+ 1.0 (sqrt (+ x 1.0)))
51.0ms
(sqrt (+ x 1.0))
215.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts
80 → 80
Iterations

Useful iterations: done (1.5s)

IterNodesCost
014323232
133318652
2119317946
done500417676

prune368.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(* (sqrt (+ x 1.0)) (+ x 1.0))
0.2b
(/ x (+ 1.0 (cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))))
8.3b
(cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
26×add-sqr-sqrt
17×add-cube-cbrt
14×flip3-+ sqrt-div flip-+
12×times-frac
11×pow1
9×sqrt-prod
8×frac-times cbrt-div add-cbrt-cube add-exp-log
7×associate-*l* distribute-lft-out
4×expm1-log1p-u associate-/r* associate-*r* associate-*l/ associate-*r/ log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 associate-/l*
2×pow-plus cube-unmult associate-/r/ pow-prod-up unswap-sqr
1×cbrt-prod distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in pow1/3 div-exp pow-prod-down prod-exp *-commutative rem-cbrt-cube cbrt-unprod hypot-def div-inv
Counts
4 → 115
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
56.0ms
(* (sqrt (+ x 1.0)) (+ x 1.0))
23.0ms
(/ x (+ 1.0 (cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))))
21.0ms
(cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (+ x 1.0))
100.0ms
(* (sqrt (+ x 1.0)) (+ x 1.0))
249.0ms
(/ x (+ 1.0 (cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))))
33.0ms
(cbrt (* (sqrt (+ x 1.0)) (+ x 1.0)))

simplify2.1s

Counts
127 → 127
Iterations

Useful iterations: done (2.1s)

IterNodesCost
020345713
152636926
2187635703
done500035463

prune745.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (+ 1.0 (/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
7.0b
(sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x))))
8.2b
(/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
11.6b
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
48×times-frac sqrt-prod
46×add-sqr-sqrt
43×add-cube-cbrt
10×associate-/r*
9×associate-/l*
8×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u distribute-lft-out add-log-exp
3×flip3-+ flip-+
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
1×sqrt-undiv hypot-def
Counts
4 → 133
Calls
4 calls:
188.0ms
(/ x (+ 1.0 (/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
2.0ms
(sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x))))
54.0ms
(/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
32.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(/ x (+ 1.0 (/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
81.0ms
(sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x))))
101.0ms
(/ (sqrt (fma (* 1.0 1.0) 1.0 (* x (* x x)))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
71.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify2.7s

Counts
145 → 145
Iterations

Useful iterations: done (2.6s)

IterNodesCost
023787647
152979722
2185978703
done502078408

prune818.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

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:
12.0ms
(+ 1.0 (sqrt (+ x 1.0)))
6.0ms
(sqrt (+ x 1.0))
32.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
90.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series624.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ 1.0 (sqrt (+ x 1.0)))
54.0ms
(sqrt (+ x 1.0))
358.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
143.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify2.7s

Counts
156 → 156
Iterations

Useful iterations: done (2.7s)

IterNodesCost
022154719
157245666
2198542729
done500142129

prune647.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.2b

bsearch48.0ms

Steps
ItersRangePoint
7
437153918387543.8
8.722653903301618e+16
3410021961549198.0

simplify10.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
023868
130868
done30868

end0.0ms

sample943.0ms

Algorithm
intervals
Results
698.0ms7994×body80valid
70.0ms2676×body80nan
1.0ms6×body1280valid