Details

Time bar (total: 18.6s)

sample184.0ms

Algorithm
intervals
Results
50.0ms853×body80nan
11.0ms255×body80valid
0.0ms1×body160valid

simplify38.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
06

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (- x 1))
0.5b
(* (sqrt (- x 1)) (sqrt x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×sqrt-prod
13×*-un-lft-identity
10×associate-*l*
7×pow1 add-cube-cbrt
6×associate-*r*
4×add-cbrt-cube sqrt-div add-exp-log difference-of-squares unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down
2×flip3-- difference-of-sqr-1 associate-*l/ insert-posit16 flip-- distribute-lft-out-- add-log-exp
1×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
2 → 57
Calls
2 calls:
10.0ms
(sqrt (- x 1))
22.0ms
(* (sqrt (- x 1)) (sqrt x))

series177.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (- x 1))
124.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify2.7s

Counts
63 → 63
Iterations
IterNodes
done5008
43851
31274
2539
1231
0109

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt x))
0.1b
(sqrt (sqrt x))
0.3b
(* (* (sqrt (- x 1)) (sqrt (sqrt x))) (sqrt (sqrt x)))
0.4b
(* (sqrt (- x 1)) (sqrt (sqrt x)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-prod
36×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
18×associate-*r*
16×add-cube-cbrt
13×sqrt-pow1
11×add-cbrt-cube associate-*l* add-exp-log
10×pow-prod-down
9×pow1/2
6×associate-*l/ unswap-sqr
4×rem-sqrt-square sqrt-div prod-exp cbrt-unprod insert-posit16 add-log-exp
3×sqrt-unprod
2×flip3-- *-commutative flip-- difference-of-squares
1×difference-of-sqr-1 distribute-lft-out--
Counts
4 → 112
Calls
4 calls:
2.0ms
(sqrt (sqrt x))
2.0ms
(sqrt (sqrt x))
74.0ms
(* (* (sqrt (- x 1)) (sqrt (sqrt x))) (sqrt (sqrt x)))
38.0ms
(* (sqrt (- x 1)) (sqrt (sqrt x)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(sqrt (sqrt x))
208.0ms
(sqrt (sqrt x))
65.0ms
(* (* (sqrt (- x 1)) (sqrt (sqrt x))) (sqrt (sqrt x)))
178.0ms
(* (sqrt (- x 1)) (sqrt (sqrt x)))

simplify3.1s

Counts
124 → 124
Iterations
IterNodes
done5001
33957
21317
1483
0190

prune463.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(- x (+ (/ 1/8 x) 1/2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity add-log-exp
3×add-sqr-sqrt
2×diff-log distribute-lft-out--
1×pow1 sum-log sub-neg flip3-- add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out associate--r+ difference-of-squares
Counts
1 → 18
Calls
1 calls:
23.0ms
(- x (+ (/ 1/8 x) 1/2))

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(- x (+ (/ 1/8 x) 1/2))

simplify1.8s

Counts
21 → 21
Iterations
IterNodes
done5000
31176
2377
1105
043

prune50.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- x 1) (sqrt (sqrt x)))
0.2b
(* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))
0.3b
(* (cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x)))))) (sqrt (sqrt x)))
29.8b
(cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt associate-*l/
31×sqrt-prod
22×associate-*r/
21×associate-*l*
20×*-un-lft-identity
19×flip3-- associate-*r* flip--
18×sqrt-div
16×cbrt-div
14×add-cube-cbrt
13×pow1 add-exp-log
12×frac-times add-cbrt-cube
6×unswap-sqr
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp difference-of-squares
3×*-commutative
2×cbrt-prod difference-of-sqr-1 distribute-lft-out--
1×pow1/3
Counts
4 → 121
Calls
4 calls:
20.0ms
(* (- x 1) (sqrt (sqrt x)))
87.0ms
(* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))
128.0ms
(* (cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x)))))) (sqrt (sqrt x)))
106.0ms
(cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
396.0ms
(* (- x 1) (sqrt (sqrt x)))
280.0ms
(* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))
219.0ms
(* (cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x)))))) (sqrt (sqrt x)))
204.0ms
(cbrt (* (sqrt x) (* (sqrt (- x 1)) (* (- x 1) (sqrt (sqrt x))))))

simplify2.5s

Counts
133 → 133
Iterations
IterNodes
done5012
22574
1801
0303

prune826.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
08

end0.0ms

sample4.1s

Algorithm
intervals
Results
3.0s24677×body80nan
685.0ms7992×body80valid
1.0ms8×body160valid