Details

Time bar (total: 14.8s)

sample105.0ms

Algorithm
intervals
Results
40.0ms238×body160nan
20.0ms498×body80nan
13.0ms256×body80valid

simplify27.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
31.3b
(sqrt (- (* x x) 1.0))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
44.0ms
(+ x (sqrt (- (* x x) 1.0)))
17.0ms
(- (* x x) 1.0)
35.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
22.0ms
(sqrt (- (* x x) 1.0))

series468.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ x (sqrt (- (* x x) 1.0)))
46.0ms
(- (* x x) 1.0)
262.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
60.0ms
(sqrt (- (* x x) 1.0))

simplify1.5s

Counts
68 → 68

prune311.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b
(sqrt (- x (sqrt 1.0)))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×add-exp-log associate-*l*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×frac-times flip3-- flip-- difference-of-squares unswap-sqr
3×log-prod sqrt-pow1 pow1/2 pow-prod-down
2×log-div associate-*r/ associate-*l/ distribute-lft-out--
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 85
Calls
4 calls:
11.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
11.0ms
(sqrt (- x (sqrt 1.0)))
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
62.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
222.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
129.0ms
(sqrt (- x (sqrt 1.0)))
424.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
280.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify751.0ms

Counts
97 → 97

prune445.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0))))))
0.5b
(cbrt (- x (sqrt 1.0)))
0.5b
(cbrt (- x (sqrt 1.0)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
20×*-un-lft-identity
19×cbrt-prod
18×sqrt-prod
14×sqrt-div
13×associate-*r*
12×add-cube-cbrt cbrt-div
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/ associate-*l*
6×flip3-- flip-- difference-of-squares
4×frac-times pow-prod-down prod-exp cbrt-unprod add-log-exp
3×flip3-+ flip-+ distribute-lft-out-- unswap-sqr
2×pow1/3 associate-*l/ *-commutative
1×distribute-lft-out
Counts
4 → 93
Calls
4 calls:
70.0ms
(* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0)))))
105.0ms
(* (sqrt (+ x (sqrt 1.0))) (* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0))))))
8.0ms
(cbrt (- x (sqrt 1.0)))
8.0ms
(cbrt (- x (sqrt 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
267.0ms
(* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0)))))
514.0ms
(* (sqrt (+ x (sqrt 1.0))) (* (fabs (cbrt (- x (sqrt 1.0)))) (sqrt (cbrt (- x (sqrt 1.0))))))
246.0ms
(cbrt (- x (sqrt 1.0)))
205.0ms
(cbrt (- x (sqrt 1.0)))

simplify1.3s

Counts
105 → 105

prune669.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.09375 (/ 1 (pow x 4)))
0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (* 0.09375 (/ 1 (pow x 4)))))
0.4b
(/ 1 (pow x 4))

rewrite597.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
94×add-sqr-sqrt
85×*-un-lft-identity
79×add-cube-cbrt
38×add-exp-log
25×associate-*r*
23×unpow-prod-down
16×add-cbrt-cube associate-/l*
15×div-exp
10×prod-exp associate-/r*
9×add-log-exp sqr-pow
8×associate--l+
7×pow1 associate-+r+ div-inv unswap-sqr
6×pow-to-exp rec-exp log-prod 1-exp pow-exp
5×cbrt-undiv
3×associate-+l+ diff-log associate-*l* sum-log
2×sub-neg frac-2neg clear-num cbrt-unprod distribute-lft-out
1×+-commutative associate-+r- pow-flip flip3-+ associate-*r/ pow-prod-down log-pow un-div-inv *-commutative flip-+ associate-/l/ inv-pow
Counts
4 → 207
Calls
4 calls:
24.0ms
(* 0.09375 (/ 1 (pow x 4)))
16.0ms
(/ (/ 0.25 x) x)
526.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (* 0.09375 (/ 1 (pow x 4)))))
17.0ms
(/ 1 (pow x 4))

series324.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* 0.09375 (/ 1 (pow x 4)))
28.0ms
(/ (/ 0.25 x) x)
204.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (* 0.09375 (/ 1 (pow x 4)))))
39.0ms
(/ 1 (pow x 4))

simplify1.2s

Counts
219 → 219

prune789.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify39.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s7750×body160nan
887.0ms16336×body80nan
512.0ms8000×body80valid