Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	446×	body	80	nan
11.0ms	196×	body	160	nan
10.0ms	256×	body	80	valid

simplify3.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.5b	(log (+ x (sqrt (- (* x x) 1.0))))
29.8b	(sqrt (- (* x x) 1.0))

rewrite75.0ms

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:

9.0ms	(- (* x x) 1.0)
19.0ms	(+ x (sqrt (- (* x x) 1.0)))
19.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
26.0ms	(sqrt (- (* x x) 1.0))

series375.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* x x) 1.0)
72.0ms	(+ x (sqrt (- (* x x) 1.0)))
203.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
56.0ms	(sqrt (- (* x x) 1.0))

simplify135.0ms

Counts: 68 → 68

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (/ (/ 0.25 x) x))
0.1b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b	(/ 0.09375 (pow x 4))

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
88×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
16×	`associate-/l*`
14×	`add-exp-log`
12×	`unpow-prod-down` `distribute-lft-out--`
11×	`pow1` `associate--l+` `add-cbrt-cube`
10×	`associate-/r*` `add-log-exp`
9×	`log-prod`
8×	`distribute-lft-out`
7×	`associate-+r+` `log-pow`
6×	`div-exp` `div-inv`
4×	`cbrt-undiv` `diff-log` `sqr-pow`
3×	`sub-neg` `associate-+l+` `sum-log` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `flip--` `flip-+` `associate-/l/`

Counts

4 → 167

Calls

4 calls:

26.0ms	(- (log x) (/ (/ 0.25 x) x))
12.0ms	(/ (/ 0.25 x) x)
445.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
8.0ms	(/ 0.09375 (pow x 4))

series523.0ms

Counts

4 → 12

Calls

4 calls:

351.0ms	(- (log x) (/ (/ 0.25 x) x))
32.0ms	(/ (/ 0.25 x) x)
102.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
39.0ms	(/ 0.09375 (pow x 4))

simplify55.0ms

Counts: 179 → 179

prune479.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

6.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
60.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series662.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
299.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
210.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Counts: 76 → 76

prune232.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
0.6b	(cbrt (sqrt (+ x (sqrt 1.0))))
0.6b	(cbrt (sqrt (+ x (sqrt 1.0))))
0.6b	(cbrt (sqrt (+ x (sqrt 1.0))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

65.0ms	(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
7.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))
7.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))
7.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
140.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))
135.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))
140.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))

simplify44.0ms

Counts: 132 → 132

prune441.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	15979×	body	80	nan
554.0ms	7619×	body	160	nan
296.0ms	8000×	body	80	valid