Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	82×	body	80	nan

simplify14.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

37.0ms	(+ 1.0 (sqrt (+ x 1.0)))
51.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series236.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
189.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify590.0ms

Counts: 51 → 51

prune111.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.5b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

53.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
11.0ms	(pow (sqrt (+ x 1.0)) 3)
42.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
122.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
97.0ms	(pow (sqrt (+ x 1.0)) 3)
95.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
283.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.7s

Counts: 196 → 196

prune559.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.5b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
127×	`*-un-lft-identity`
96×	`sqrt-div`
76×	`add-sqr-sqrt`
70×	`flip3-+` `flip-+`
66×	`associate-*r/`
65×	`associate-l`
63×	`associate-*l/`
59×	`add-cube-cbrt`
58×	`associate-/r/`
52×	`frac-sub`
36×	`add-exp-log`
33×	`distribute-lft-out`
29×	`add-cbrt-cube`
26×	`sqrt-prod`
21×	`pow1`
14×	`frac-times` `div-exp`
13×	`associate-/l*`
11×	`swap-sqr` `div-inv`
10×	`cbrt-undiv` `flip3--` `associate-r` `prod-exp` `flip--`
8×	`sqrt-pow1` `pow1/2`
7×	`cbrt-unprod`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`pow-prod-down` `associate-/r*` `sub-div`
3×	`pow-sqr`
2×	`1-exp` `*-commutative`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `pow-plus` `sqrt-unprod` `diff-log` `clear-num` `rem-square-sqrt` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

485.0ms	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
975.0ms	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
38.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
50.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

583.0ms	(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
381.0ms	(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
31.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
86.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify1.0s

Counts: 284 → 284

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
50×	`add-cbrt-cube`
36×	`prod-exp`
30×	`div-exp`
20×	`*-un-lft-identity`
19×	`associate-*r/`
17×	`cbrt-unprod`
16×	`cbrt-undiv` `associate-/r/`
15×	`flip3-+` `flip-+`
14×	`add-sqr-sqrt` `times-frac`
13×	`associate-l` `associate-*l/`
12×	`add-cube-cbrt` `sqrt-div` `frac-sub`
10×	`1-exp` `associate-r`
6×	`pow1` `associate-/l/` `add-log-exp`
5×	`associate-/r*`
4×	`div-inv` `distribute-lft-out` `associate-/l*`
3×	`flip3--` `flip--`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `pow-prod-down` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

15.0ms	(+ 1.0 (sqrt (+ x 1.0)))
1.1s	(* (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (/ (* 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (+ 1.0 (sqrt (+ x 1.0)))))
177.0ms	(/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1))
227.0ms	(/ (* 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (+ 1.0 (sqrt (+ x 1.0))))

series946.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ 1.0 (sqrt (+ x 1.0)))
225.0ms	(* (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (/ (* 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (+ 1.0 (sqrt (+ x 1.0)))))
317.0ms	(/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1))
335.0ms	(/ (* 1 (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0))))) (+ 1.0 (sqrt (+ x 1.0))))

simplify757.0ms

Counts: 145 → 145

prune592.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

-39.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify650.0ms

end0.0ms

sample888.0ms

Algorithm

intervals

Results

449.0ms	8000×	body	80	valid
139.0ms	2751×	body	80	nan