Details

sample203.0ms

Algorithm

intervals

Results

47.0ms	61×	body	10240	exit
46.0ms	38×	body	640	valid
38.0ms	55×	body	1280	valid
33.0ms	325×	body	80	valid
7.0ms	21×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (101.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
3.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
34×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-log-exp`
12×	`difference-of-squares`
11×	`distribute-lft-out--`
6×	`add-cbrt-cube` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`associate-/r*`
2×	`exp-prod` `flip3--` `diff-log` `div-sub` `flip--` `rem-exp-log` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `div-inv` `associate--r-`

Counts

4 → 87

Calls

4 calls:

71.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
14.0ms	(exp (* (- 1.0 eps) x))
7.0ms	(exp (* (+ 1.0 eps) x))
267.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
23.0ms	(exp (* (- 1.0 eps) x))
21.0ms	(exp (* (+ 1.0 eps) x))
264.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.9s

Counts

99 → 99

Iterations

Useful iterations: 3 (802.0ms)

Iter	Nodes	Cost
0	182	2161
1	424	2075
2	1008	1949
3	3402	1913
done	5000	1913

prune371.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

34.0ms

(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

series101.0ms

Counts

1 → 3

Calls

1 calls:

101.0ms

(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

simplify1.6s

Counts

36 → 36

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	69	467
1	161	440
2	543	385
3	2157	385
done	5001	385

prune86.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
34.9b	(cbrt (pow x 2))
34.9b	(cbrt (pow x 2))
34.9b	(cbrt (pow x 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
52×	`add-sqr-sqrt`
31×	`unpow-prod-down`
25×	`unswap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
17×	`unpow2` `sqr-pow`
11×	`pow1` `swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

32.0ms	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))
2.0ms	(cbrt (pow x 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

299.0ms	(* (cbrt (pow x 2)) (cbrt (pow x 2)))
276.0ms	(cbrt (pow x 2))
264.0ms	(cbrt (pow x 2))
247.0ms	(cbrt (pow x 2))

simplify2.3s

Counts

136 → 136

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	104	1554
1	166	1381
2	349	1031
3	743	965
4	2503	959
done	5001	922

prune572.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 4 expressions with local error:

34.9b	(cbrt (* x x))
34.9b	(cbrt (* x x))
34.9b	(cbrt (* x x))
34.9b	(cbrt (pow x 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
1×	`unpow2` `sqr-pow`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* x x))
3.0ms	(cbrt (* x x))
4.0ms	(cbrt (* x x))
2.0ms	(cbrt (pow x 2))

series1.8s

Counts

4 → 12

Calls

4 calls:

791.0ms	(cbrt (* x x))
348.0ms	(cbrt (* x x))
326.0ms	(cbrt (* x x))
306.0ms	(cbrt (pow x 2))

simplify2.0s

Counts

55 → 55

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	47	342
1	76	333
2	122	284
3	241	271
4	885	271
done	5001	271

prune330.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

regimes139.0ms

Accuracy

91.7% (1.4b remaining)

Error of 1.8b against oracle of 0.4b and baseline of 17.2b

bsearch205.0ms

Steps

Iters	Range		Point
8	2.1318049287245128e-27	3.447572751372202e-23	3.375282683015706e-23

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	88
1	52	88
done	52	88

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.7s	2007×	body	10240	exit
2.5s	1653×	body	1280	valid
1.7s	10148×	body	80	valid
737.0ms	1247×	body	640	valid
259.0ms	618×	body	320	valid
71.0ms	347×	body	160	valid