Details

Time bar (total: 13.1s)

sample108.0ms

Algorithm
intervals
Results
66.0ms660×body80nan
24.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done20
320
218
114
09

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(/ (sqrt (- 1 (* x x))) x)
0.2b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
59×times-frac
50×add-sqr-sqrt
38×add-cube-cbrt
31×sqrt-prod
16×distribute-lft-out
15×log-prod
14×div-inv
13×fma-def
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×log-div associate-/r*
2×flip3-+ flip3-- frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp log-pow
Counts
4 → 142
Calls
4 calls:
16.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
8.0ms
(sqrt (- 1 (* x x)))
31.0ms
(/ (sqrt (- 1 (* x x))) x)
21.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
71.0ms
(sqrt (- 1 (* x x)))
102.0ms
(/ (sqrt (- 1 (* x x))) x)
181.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

simplify967.0ms

Counts
154 → 154
Iterations
IterNodes
done2000
21579
1554
0247

prune657.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1 (* x x)))
0.0b
(+ 1 (sqrt (- 1 (* x x))))
0.2b
(log (* (/ 1 x) (+ 1 (sqrt (- 1 (* x x))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
9×*-un-lft-identity
8×add-sqr-sqrt
7×pow1
6×sqrt-prod
5×log-div rem-log-exp add-cube-cbrt add-log-exp
4×prod-exp
3×expm1-log1p-u fma-def flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u
2×frac-times sqrt-div div-exp associate-*r/ log-pow distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square rec-exp log-prod sum-log sqrt-pow1 flip3-- pow1/2 1-exp pow-prod-down associate-*l/ flip--
Counts
3 → 62
Calls
3 calls:
5.0ms
(sqrt (- 1 (* x x)))
9.0ms
(+ 1 (sqrt (- 1 (* x x))))
24.0ms
(log (* (/ 1 x) (+ 1 (sqrt (- 1 (* x x))))))

series368.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(sqrt (- 1 (* x x)))
50.0ms
(+ 1 (sqrt (- 1 (* x x))))
248.0ms
(log (* (/ 1 x) (+ 1 (sqrt (- 1 (* x x))))))

simplify898.0ms

Counts
71 → 71
Iterations
IterNodes
done2000
21032
1385
0146

prune411.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1 (* x x)))
0.0b
(log1p (sqrt (- 1 (* x x))))
0.2b
(- (log1p (sqrt (- 1 (* x x)))) (log x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
12×prod-diff
8×pow1
5×sqrt-prod
4×expm1-log1p-u log-pow add-log-exp
3×log-prod add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate--r+ difference-of-squares
2×log1p-udef flip3-- sqrt-div diff-log flip-- distribute-lft-out--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 log1p-expm1
Counts
3 → 69
Calls
3 calls:
7.0ms
(sqrt (- 1 (* x x)))
0.0ms
(log1p (sqrt (- 1 (* x x))))
6.0ms
(- (log1p (sqrt (- 1 (* x x)))) (log x))

series444.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(sqrt (- 1 (* x x)))
148.0ms
(log1p (sqrt (- 1 (* x x))))
236.0ms
(- (log1p (sqrt (- 1 (* x x)))) (log x))

simplify673.0ms

Counts
78 → 78
Iterations
IterNodes
done2001
21047
1387
0169

prune290.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (- 1 (* x x))))
0.0b
(expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))
0.2b
(log (* (/ 1 x) (expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))))
1.0b
(log1p (+ 1 (sqrt (- 1 (* x x)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
8×*-un-lft-identity
7×pow1
6×add-sqr-sqrt add-log-exp
5×expm1-log1p-u rem-log-exp add-cube-cbrt
4×add-cbrt-cube prod-exp insert-posit16 log1p-expm1-u
3×fma-def
2×div-exp log-pow distribute-lft-out
1×+-commutative log-div rec-exp log1p-udef log-prod expm1-log1p sum-log flip3-+ 1-exp pow-prod-down associate-*l/ log1p-expm1 sqrt-prod flip-+ expm1-udef
Counts
4 → 62
Calls
4 calls:
9.0ms
(+ 1 (sqrt (- 1 (* x x))))
0.0ms
(expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))
7.0ms
(log (* (/ 1 x) (expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))))
0.0ms
(log1p (+ 1 (sqrt (- 1 (* x x)))))

series739.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ 1 (sqrt (- 1 (* x x))))
179.0ms
(expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))
392.0ms
(log (* (/ 1 x) (expm1 (log1p (+ 1 (sqrt (- 1 (* x x))))))))
126.0ms
(log1p (+ 1 (sqrt (- 1 (* x x)))))

simplify916.0ms

Counts
74 → 74
Iterations
IterNodes
done2000
21297
1433
0170

prune427.0ms

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

simplify2.0ms

Iterations
IterNodes
done10
110
08

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.0s23875×body80nan
1.9s8000×body80valid