Details

sample195.0ms

Algorithm

intervals

Results

93.0ms	193×	body	10240	exit
19.0ms	413×	body	80	nan
10.0ms	236×	body	80	valid
3.0ms	24×	body	160	valid

simplify850.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	767
5	185
4	76
3	41
2	28
1	19
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
4.5b	(- (pow (exp 2.0) x) 1.0)
4.7b	(- (exp x) 1.0)

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
71×	`times-frac`
53×	`add-cube-cbrt`
52×	`difference-of-squares`
41×	`sqrt-prod`
30×	`prod-diff`
28×	`distribute-lft-out--`
24×	`unpow-prod-down`
16×	`sqr-pow`
10×	`fma-neg`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*` `flip3--` `flip--`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 195

Calls

4 calls:

97.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
63.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
24.0ms	(- (pow (exp 2.0) x) 1.0)
13.0ms	(- (exp x) 1.0)

series394.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0))
190.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (- (exp x) 1.0)))
79.0ms	(- (pow (exp 2.0) x) 1.0)
38.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

207 → 207

Iterations

Iter	Nodes
done	5001
2	2187
1	636
0	296

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
0.2b	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
4.5b	(fma 1.0 (- 1.0) (exp (+ x x)))
4.5b	(- (pow (exp 2.0) x) 1.0)

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

435×	`times-frac`
373×	`add-sqr-sqrt`
343×	`*-un-lft-identity`
177×	`add-cube-cbrt`
131×	`sqrt-prod`
114×	`difference-of-squares`
50×	`unpow-prod-down`
45×	`distribute-lft-out`
42×	`sqr-pow`
38×	`distribute-lft-out--`
32×	`associate-/r/`
21×	`prod-diff`
18×	`associate-/r*`
17×	`div-inv`
15×	`flip3-+` `flip-+`
9×	`add-cbrt-cube` `add-exp-log`
7×	`fma-neg` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
2×	`flip3--` `flip--` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-sub` `fma-udef`

Counts

4 → 373

Calls

4 calls:

71.0ms	(/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
49.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
0.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
22.0ms	(- (pow (exp 2.0) x) 1.0)

series642.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
285.0ms	(sqrt (/ (- (pow (exp 2.0) x) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
62.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
75.0ms	(- (pow (exp 2.0) x) 1.0)

simplify770.0ms

Counts

385 → 385

Iterations

Iter	Nodes
done	5000
1	1363
0	577

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (/ (* (- (exp (* x 2.0)) 1.0) (+ (pow (exp x) 3) (pow 1.0 3))) (fma 1.0 (- 1.0) (pow (exp 2) x))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
4.5b	(- (exp (* x 2.0)) 1.0)
4.5b	(fma 1.0 (- 1.0) (pow (exp 2) x))
4.7b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `sqrt-prod`
25×	`add-cube-cbrt`
10×	`prod-diff`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u` `div-inv`
2×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--`
1×	`sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `sqrt-div` `flip-+` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

94.0ms	(sqrt (/ (/ (* (- (exp (* x 2.0)) 1.0) (+ (pow (exp x) 3) (pow 1.0 3))) (fma 1.0 (- 1.0) (pow (exp 2) x))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
11.0ms	(- (exp (* x 2.0)) 1.0)
0.0ms	(fma 1.0 (- 1.0) (pow (exp 2) x))
10.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series595.0ms

Counts

4 → 12

Calls

4 calls:

377.0ms	(sqrt (/ (/ (* (- (exp (* x 2.0)) 1.0) (+ (pow (exp x) 3) (pow 1.0 3))) (fma 1.0 (- 1.0) (pow (exp 2) x))) (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
44.0ms	(- (exp (* x 2.0)) 1.0)
116.0ms	(fma 1.0 (- 1.0) (pow (exp 2) x))
58.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	2802
1	664
0	285

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
0.2b	(sqrt (/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
4.5b	(fma 1.0 (- 1.0) (exp (+ x x)))
4.5b	(- (exp (* x 2.0)) 1.0)

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

1167×	`times-frac`
856×	`*-un-lft-identity`
646×	`add-sqr-sqrt`
600×	`cbrt-prod`
472×	`add-cube-cbrt`
347×	`sqrt-prod`
187×	`unpow-prod-down` `cube-prod`
117×	`distribute-lft-out`
80×	`associate-/r/`
75×	`distribute-lft-out--` `difference-of-squares`
41×	`div-inv`
39×	`flip3-+` `flip-+` `sqr-pow`
37×	`cube-mult` `unpow3`
19×	`associate-/l*`
18×	`associate-/r*`
11×	`rem-sqrt-square`
9×	`prod-diff` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `div-exp`
2×	`cube-div` `cbrt-div` `flip3--` `flip--` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `fma-udef`

Counts

4 → 806

Calls

4 calls:

76.0ms	(/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
86.0ms	(sqrt (/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
0.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
19.0ms	(- (exp (* x 2.0)) 1.0)

series520.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
231.0ms	(sqrt (/ (cbrt (pow (- (exp (* x 2.0)) 1.0) 3)) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))))
77.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
35.0ms	(- (exp (* x 2.0)) 1.0)

simplify890.0ms

Counts

818 → 818

Iterations

Iter	Nodes
done	5001
1	1738
0	887

prune3.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes42.0ms

Accuracy

74.9% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 3.0b

bsearch66.0ms

Steps

Iters	Range		Point
4	-1.2620558025192223e-10	-6.638792125712922e-11	-1.0586348953815684e-10

simplify7.0ms

Iterations

Iter	Nodes
done	47
1	47
0	41

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.3s	6821×	body	10240	exit
1.1s	7393×	body	80	valid
953.0ms	12777×	body	80	nan
103.0ms	723×	body	160	valid