Details

sample277.0ms

Algorithm

intervals

Results

94.0ms	206×	body	10240	exit
89.0ms	401×	body	80	nan
18.0ms	240×	body	80	valid
3.0ms	19×	body	160	valid

simplify1.2s

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	185	12
6	764	12
done	5000	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize14.0ms

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))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp x) 1.0)

rewrite144.0ms

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:

32.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
22.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

series255.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
64.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

167 → 167

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	232	2954
1	503	2694
2	1532	2473
done	5000	2423

prune598.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite186.0ms

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×	`pow1` `fma-neg`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `exp-sum` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

60.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
19.0ms	(+ (exp x) 1.0)
25.0ms	(- (exp (* 2.0 x)) 1.0)
78.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series271.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
14.0ms	(+ (exp x) 1.0)
41.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	183	1444
1	461	1307
2	1811	1154
done	5003	1098

prune547.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp (+ x x)) (* 1.0 1.0))
4.1b	(- 1.0 (exp x))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`prod-diff`
10×	`fma-neg` `add-log-exp`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `exp-sum` `flip--`
2×	`distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

8.0ms	(pow (exp x) 3)
27.0ms	(- (exp (* 2.0 x)) 1.0)
75.0ms	(- (exp (+ x x)) (* 1.0 1.0))
9.0ms	(- 1.0 (exp x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp x) 3)
41.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp (+ x x)) (* 1.0 1.0))
26.0ms	(- 1.0 (exp x))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: 2 (544.0ms)

Iter	Nodes	Cost
0	201	1421
1	523	1121
2	2483	940
done	5000	940

prune805.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* 2.0 x)))
0.2b	(sqrt (exp (* 2.0 x)))
4.1b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.2b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-prod`
76×	`add-sqr-sqrt`
72×	`prod-diff`
66×	`*-un-lft-identity`
58×	`add-cube-cbrt`
12×	`fma-neg`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`pow1` `sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 158

Calls

4 calls:

7.0ms	(sqrt (exp (* 2.0 x)))
7.0ms	(sqrt (exp (* 2.0 x)))
45.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
48.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series211.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (exp (* 2.0 x)))
44.0ms	(sqrt (exp (* 2.0 x)))
60.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
71.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify3.5s

Counts

170 → 170

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	170	3420
1	355	2480
2	928	1946
3	4599	1646
done	5000	1646

prune695.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

77.7% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 3.0b

bsearch39.0ms

Steps

Iters	Range		Point
6	-8.253445947576724e-07	-8.551954805789552e-08	-8.130656909693609e-07

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	27	35
done	27	35

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.6s	6902×	body	10240	exit
1.4s	12606×	body	80	nan
1.1s	7372×	body	80	valid
109.0ms	739×	body	160	valid