Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	79×	body	1280	valid
9.0ms	91×	body	10240	exit
6.0ms	57×	body	640	valid
2.0ms	88×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4
done	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
4.1b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

17.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series48.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
19.0ms	(- (exp x) 1.0)

simplify178.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (172.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404
done	5001	404

prune149.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

5.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms	(fma 1/12 x (/ 1 x))

series69.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
52.0ms	(fma 1/12 x (/ 1 x))

simplify36.0ms

Counts

34 → 34

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116
done	5001	116

prune67.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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 → 103

Calls

4 calls:

37.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))
4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))

series289.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))
78.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
72.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
78.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))

simplify46.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	330	1259
1	1109	1189
2	5001	1083
done	5001	1083

prune298.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod`
17×	`*-un-lft-identity`
10×	`cbrt-div`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 67

Calls

4 calls:

4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
4.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
9.0ms	(cbrt (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
78.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
78.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
50.0ms	(cbrt (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

simplify67.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	272	784
1	677	741
2	2569	701
3	5001	650
done	5001	650

prune276.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

96.8% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13
done	24	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

381.0ms	2245×	body	1280	valid
275.0ms	2597×	body	10240	exit
171.0ms	1643×	body	640	valid
60.0ms	890×	body	320	valid
55.0ms	2838×	body	80	valid
17.0ms	384×	body	160	valid