Details

sample190.0ms

Algorithm

intervals

Results

53.0ms	48×	body	640	valid
36.0ms	60×	body	10240	exit
31.0ms	52×	body	1280	valid
30.0ms	359×	body	80	valid
3.0ms	12×	body	320	valid
2.0ms	13×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	335	27
4	933	27
5	4084	27
done	5000	27

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
2.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite502.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
24×	`times-frac`
15×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out--`
7×	`add-exp-log`
6×	`pow1` `distribute-lft-out`
5×	`associate-l` `difference-of-squares`
4×	`associate-/l*`
3×	`associate-r` `associate-/r*`
2×	`flip3--` `exp-to-pow` `diff-log` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `exp-prod` `frac-2neg` `flip3-+` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `rem-exp-log` `associate--r-` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

44.0ms	(* (- 1.0 eps) x)
99.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
17.0ms	(exp (* (- 1.0 eps) x))
337.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- 1.0 eps) x)
76.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
24.0ms	(exp (* (- 1.0 eps) x))
250.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify2.8s

Counts

101 → 101

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	187	2022
1	439	1940
2	1173	1810
3	4015	1765
done	5001	1763

prune470.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x 0.6666666666666667) 1.0)
0.0b	(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`add-cube-cbrt` `sub-neg` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
1×	`diff-log` `associate-l` `*-commutative` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

11.0ms	(- (* x 0.6666666666666667) 1.0)
94.0ms	(* (* x x) (- (* x 0.6666666666666667) 1.0))

series166.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x 0.6666666666666667) 1.0)
107.0ms	(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify2.0s

Counts

43 → 43

Iterations

Useful iterations: 3 (939.0ms)

Iter	Nodes	Cost
0	67	495
1	176	469
2	600	409
3	2214	407
done	5000	407

prune103.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b	(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b	(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

7.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
13.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
13.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
101.0ms	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
211.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
211.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
236.0ms	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

simplify3.0s

Counts

99 → 99

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	183	2139
1	438	2008
2	1319	1905
3	4752	1623
done	5000	1545

prune468.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.2b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.2b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.3b	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-div`
9×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

14.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
14.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
14.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
29.0ms	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

series1.1s

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
274.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
232.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
382.0ms	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

simplify901.0ms

Counts

84 → 84

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	188	1804
1	452	1685
2	1362	1603
done	5000	1470

prune578.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

regimes144.0ms

Accuracy

92.8% (1.2b remaining)

Error of 1.7b against oracle of 0.5b and baseline of 16.8b

bsearch293.0ms

Steps

Iters	Range		Point
7	7.705379630644969e-17	8.69103209592137e-15	8.501320620640499e-15

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	44	95
1	55	95
done	55	95

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.8s	1949×	body	10240	exit
2.2s	1754×	body	1280	valid
1.9s	9945×	body	80	valid
809.0ms	1251×	body	640	valid
200.0ms	612×	body	320	valid
77.0ms	343×	body	160	valid