Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	80×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

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))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
34.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series180.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
139.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts

58 → 58

Iterations

Useful iterations: 3 (582.0ms)

Iter	Nodes	Cost
0	121	771
1	289	722
2	872	665
3	3751	657
done	5000	657

prune125.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
15×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow1/3` `distribute-lft-out` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 79

Calls

4 calls:

41.0ms	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
17.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series4.7s

Counts

4 → 12

Calls

4 calls:

4.0s	(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
224.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
230.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
235.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify956.0ms

Counts

91 → 91

Iterations

Useful iterations: done (952.0ms)

Iter	Nodes	Cost
0	228	2136
1	620	1948
2	2241	1720
done	5001	1628

prune261.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.4b	(- (* (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)))

rewrite180.0ms

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×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `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` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

10.0ms	(pow (sqrt (+ x 1.0)) 3)
41.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
91.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (sqrt (+ x 1.0)) 3)
17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
66.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
190.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.4s

Counts

206 → 206

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	326	4145
1	804	2987
2	2940	2729
done	5000	2724

prune458.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.4b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

rewrite225.0ms

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` `add-cbrt-cube` `associate-/l*`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `associate-/r*` `pow-sqr`
2×	`cube-div` `associate-/l/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

11.0ms	(pow (sqrt (+ x 1.0)) 3)
40.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
136.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

series270.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (sqrt (+ x 1.0)) 3)
24.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
59.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
126.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) x)

simplify1.9s

Counts

206 → 206

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	314	4125
1	771	3013
2	2754	2751
done	5000	2748

prune465.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

99.2% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.9b

bsearch31.0ms

Steps

Iters	Range		Point
8	1126179.5725289274	335341194.4438158	28329089.96762624

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	49
1	29	49
done	29	49

end0.0ms

sample355.0ms

Algorithm

intervals

Results

156.0ms	7994×	body	80	valid
43.0ms	2681×	body	80	nan
1.0ms	6×	body	1280	valid