Details

sample55.0ms

Algorithm

intervals

Results

13.0ms	220×	body	160	nan
13.0ms	461×	body	80	nan
9.0ms	256×	body	80	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
31.0b	(sqrt (- (* x x) 1.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

28.0ms	(+ x (sqrt (- (* x x) 1.0)))
44.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
15.0ms	(sqrt (- (* x x) 1.0))

series349.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ x (sqrt (- (* x x) 1.0)))
210.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
68.0ms	(sqrt (- (* x x) 1.0))

simplify80.0ms

Counts: 52 → 52

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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:

5.0ms	(+ 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))))))
55.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series818.0ms

Counts

3 → 9

Calls

3 calls:

208.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
345.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
264.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify52.0ms

Counts: 76 → 76

prune333.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.2b	(log (+ x (* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-div`
50×	`sqrt-prod`
33×	`add-sqr-sqrt`
32×	`frac-times`
23×	`*-un-lft-identity` `flip3-+` `flip-+`
20×	`associate-l`
19×	`pow1`
16×	`associate-*r/`
15×	`add-cube-cbrt`
12×	`add-exp-log` `flip3--` `flip--`
11×	`add-cbrt-cube`
10×	`associate-r` `pow-prod-down` `associate-*l/`
9×	`sqrt-pow1`
7×	`pow1/2`
6×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `sqrt-unprod` `distribute-lft-out`
2×	`rem-sqrt-square` `log-div` `*-commutative` `difference-of-squares`
1×	`rem-log-exp` `log-pow` `distribute-lft-out--`

Counts

4 → 137

Calls

4 calls:

19.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
7.0ms	(log (+ x (* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))))
155.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
104.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

216.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
419.0ms	(log (+ x (* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))))
210.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
545.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify100.0ms

Counts: 149 → 149

prune649.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
0.2b	(- (log 2) (log (/ 1 x)))
0.3b	(/ (* 1/4 1.0) (pow x 2))
0.4b	(/ (pow (sqrt 1.0) 4) (pow x 4))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

169×	`unpow-prod-down` `times-frac`
138×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
105×	`add-cube-cbrt`
74×	`associate-r`
52×	`add-exp-log`
48×	`sqrt-prod`
45×	`sqr-pow`
24×	`div-exp`
16×	`log-prod` `add-cbrt-cube`
15×	`associate-/r*`
14×	`pow-to-exp` `pow-exp`
13×	`prod-exp` `associate--r+` `unswap-sqr`
11×	`associate-/l*`
10×	`pow1`
4×	`cbrt-undiv` `log-pow` `div-inv` `distribute-lft-out--` `add-log-exp`
3×	`associate-l` `associate--l+` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `unpow2`
1×	`sub-neg` `log-div` `flip3--` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `flip--` `associate--r-` `difference-of-squares`

Counts

4 → 288

Calls

4 calls:

43.0ms	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
13.0ms	(- (log 2) (log (/ 1 x)))
12.0ms	(/ (* 1/4 1.0) (pow x 2))
15.0ms	(/ (pow (sqrt 1.0) 4) (pow x 4))

series710.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
333.0ms	(- (log 2) (log (/ 1 x)))
36.0ms	(/ (* 1/4 1.0) (pow x 2))
170.0ms	(/ (pow (sqrt 1.0) 4) (pow x 4))

simplify91.0ms

Counts: 300 → 300

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	16579×	body	80	nan
760.0ms	7766×	body	160	nan
433.0ms	8000×	body	80	valid