Details

sample65.0ms

Algorithm

intervals

Results

33.0ms	77×	body	1280	valid
13.0ms	55×	body	640	valid
5.0ms	19×	body	2560	valid
2.0ms	19×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	18×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) 1.0)
1.0b	(+ x (sqrt (+ (* x x) 1.0)))
3.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b	(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(+ (* x x) 1.0)
8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series305.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x x) 1.0)
59.0ms	(+ x (sqrt (+ (* x x) 1.0)))
167.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms	(sqrt (+ (* x x) 1.0))

simplify1.9s

Counts

65 → 65

Iterations

Useful iterations: 3 (432.0ms)

Iter	Nodes	Cost
0	141	885
1	334	812
2	1057	719
3	4910	703
done	5000	703

prune187.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

110.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
69.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series306.0ms

Counts

2 → 6

Calls

2 calls:

165.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
140.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify2.2s

Counts

292 → 292

Iterations

Useful iterations: 2 (426.0ms)

Iter	Nodes	Cost
0	336	4436
1	874	3460
2	4386	2955
done	5000	2955

prune418.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6))))
0.2b	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
2.7b	(log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
50×	`associate-l`
44×	`*-un-lft-identity`
40×	`times-frac`
33×	`add-cube-cbrt`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
11×	`add-exp-log`
9×	`pow1`
8×	`log-pow` `unswap-sqr`
6×	`log-prod` `distribute-lft-out--` `add-log-exp`
5×	`add-cbrt-cube`
4×	`prod-exp` `distribute-lft-out`
3×	`associate-r` `associate--r+`
2×	`diff-log` `pow-exp` `div-inv` `sqr-pow`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `unpow3` `div-exp` `rem-log-exp` `associate-l/` `associate--l+` `sum-log` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

3 → 113

Calls

3 calls:

286.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6))))
27.0ms	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
1.0ms	(log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

series427.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6))))
138.0ms	(* (pow (/ x (sqrt 1.0)) 3) 1/6)
137.0ms	(log (exp (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

simplify602.0ms

Counts

122 → 122

Iterations

Useful iterations: done (599.0ms)

Iter	Nodes	Cost
0	155	1770
1	396	1584
2	1630	1490
done	5000	1488

prune255.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b	(/ 0.125 (pow x 3))
11.4b	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
51×	`times-frac`
36×	`*-un-lft-identity`
30×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
11×	`add-log-exp`
10×	`add-exp-log` `difference-of-squares`
6×	`add-cbrt-cube` `sqr-pow`
5×	`pow1`
4×	`cube-mult` `unpow3`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`sub-neg` `log-div` `associate-+l+` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+l-` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `div-inv`

Counts

4 → 119

Calls

4 calls:

198.0ms	(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
31.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms	(/ 0.125 (pow x 3))
119.0ms	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
95.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
36.0ms	(/ 0.125 (pow x 3))
155.0ms	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

simplify771.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (170.0ms)

Iter	Nodes	Cost
0	220	2024
1	491	1818
2	1987	1704
done	5000	1704

prune254.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch83.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.89474849272833
10	-155084744.97222546	-0.0009113054925467739	-1.0079740505275243

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	57
1	40	57
done	40	57

end0.0ms

sample1.9s

Algorithm

intervals

Results

965.0ms	2369×	body	1280	valid
360.0ms	1561×	body	640	valid
205.0ms	758×	body	2560	valid
107.0ms	808×	body	320	valid
64.0ms	2113×	body	80	valid
30.0ms	391×	body	160	valid