Details

sample489.0ms

Algorithm

intervals

Results

165.0ms	211×	body	10240	exit
126.0ms	326×	body	80	nan
29.0ms	244×	body	80	valid
4.0ms	15×	body	160	valid

simplify7.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5038
8	4409
7	1194
6	341
5	135
4	66
3	38
2	27
1	19
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize62.0ms

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))
3.4b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite201.0ms

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:

57.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
81.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

series365.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
110.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
41.0ms	(- (exp (* 2.0 x)) 1.0)
49.0ms	(- (exp x) 1.0)

simplify4.3s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4016
2	1192
1	502
0	232

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
3.4b	(- (exp x) 1.0)
3.4b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

7.0ms	(sqrt (exp (* 2.0 x)))
40.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series489.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (exp (* 2.0 x)))
230.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
38.0ms	(- (exp x) 1.0)
173.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify4.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
3	2680
2	783
1	316
0	157

prune841.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

25.5b

(sqrt (fma x (fma x 0.5 1.0) 2.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

3.0ms

(sqrt (fma x (fma x 0.5 1.0) 2.0))

series190.0ms

Counts

1 → 3

Calls

1 calls:

189.0ms

(sqrt (fma x (fma x 0.5 1.0) 2.0))

simplify5.7s

Counts

18 → 18

Iterations

Iter	Nodes
done	5000
4	4766
3	1127
2	357
1	126
0	53

prune152.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0)))
0.3b	(* (fabs (cbrt (fma x (fma x 0.5 1.0) 2.0))) (sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0))))
26.4b	(cbrt (fma x (fma x 0.5 1.0) 2.0))
26.4b	(cbrt (fma x (fma x 0.5 1.0) 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

14.0ms	(sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0)))
30.0ms	(* (fabs (cbrt (fma x (fma x 0.5 1.0) 2.0))) (sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0))))
2.0ms	(cbrt (fma x (fma x 0.5 1.0) 2.0))
2.0ms	(cbrt (fma x (fma x 0.5 1.0) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

315.0ms	(sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0)))
285.0ms	(* (fabs (cbrt (fma x (fma x 0.5 1.0) 2.0))) (sqrt (cbrt (fma x (fma x 0.5 1.0) 2.0))))
281.0ms	(cbrt (fma x (fma x 0.5 1.0) 2.0))
297.0ms	(cbrt (fma x (fma x 0.5 1.0) 2.0))

simplify3.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1618
1	501
0	198

prune902.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

80.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.6b

bsearch70.0ms

Steps

Iters	Range		Point
6	-0.00015200343398984049	-1.963203309137196e-05	-1.9984726555003664e-05

simplify8.0ms

Iterations

Iter	Nodes
done	20
1	20
0	19

end0.0ms

sample9.7s

Algorithm

intervals

Results

6.4s	6584×	body	10240	exit
1.3s	12492×	body	80	nan
1.0s	7320×	body	80	valid
144.0ms	798×	body	160	valid