Details

sample328.0ms

Algorithm

intervals

Results

40.0ms	213×	body	10240	exit
12.0ms	389×	body	80	nan
7.0ms	233×	body	80	valid
2.0ms	25×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	175	12
6	477	12
7	1684	12
done	5001	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
30.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify524.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	232	2954
1	475	2688
2	1321	2453
done	5000	2453

prune390.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

6.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(+ (exp x) 1.0)
5.0ms	(- (exp (* 2.0 x)) 1.0)
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series88.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ (exp x) 1.0))
13.0ms	(+ (exp x) 1.0)
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify790.0ms

Counts

100 → 100

Iterations

Useful iterations: done (787.0ms)

Iter	Nodes	Cost
0	166	1120
1	360	992
2	1086	845
done	5000	763

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.3b	(log1p (- (exp (* 2.0 x)) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`fma-neg`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `exp-sum` `difference-of-squares`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`+-commutative` `log1p-udef` `flip3-+` `log1p-expm1` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
0.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series472.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
420.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.5s

Counts

92 → 92

Iterations

Useful iterations: 3 (737.0ms)

Iter	Nodes	Cost
0	146	1036
1	319	928
2	921	773
3	4697	695
done	5000	695

prune327.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (+ (exp x) 1.0))
0.3b	(log1p (- (exp (* 2.0 x)) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
7×	`fma-neg`
6×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 74

Calls

4 calls:

0.0ms	(log1p (+ (exp x) 1.0))
0.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series529.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log1p (+ (exp x) 1.0))
415.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

86 → 86

Iterations

Useful iterations: 3 (570.0ms)

Iter	Nodes	Cost
0	150	1024
1	310	918
2	878	762
3	4220	683
done	5001	683

prune343.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

74.4% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch44.0ms

Steps

Iters	Range		Point
8	-0.0008391074150366579	-8.849834202292668e-07	-1.3181801234810229e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	40
1	32	40
done	32	40

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6739×	body	10240	exit
374.0ms	12781×	body	80	nan
233.0ms	7403×	body	80	valid
59.0ms	711×	body	160	valid