Details

sample400.0ms

Algorithm

intervals

Results

43.0ms	225×	body	10240	exit
27.0ms	242×	body	80	valid
14.0ms	418×	body	80	nan
2.0ms	21×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite107.0ms

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:

40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
20.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
26.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune375.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
0.5b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
4.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.1b	(- (exp (* 2.0 x)) 1.0)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

30.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
18.0ms	(sqrt (* (/ (- (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)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series412.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
155.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5001	1028

prune337.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.2b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
24×	`times-frac`
22×	`sqrt-prod`
10×	`prod-diff`
8×	`add-log-exp`
7×	`sqrt-div`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`frac-times` `sub-neg` `flip3--` `diff-log` `associate-*r/` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sqrt-undiv` `distribute-rgt-out--` `frac-2neg` `div-exp` `associate-*l/` `clear-num` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

76.0ms	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
16.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
8.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series380.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
25.0ms	(- (exp (* 2.0 x)) 1.0)
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
31.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	565	2485
1	2160	2275
2	5001	2257

prune547.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))) (+ (exp x) 1.0)))
0.6b	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
4.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.1b	(- (exp (* 2.0 x)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`cbrt-prod`
9×	`prod-diff`
7×	`pow1`
6×	`add-log-exp`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-neg` `cube-prod`
2×	`frac-times` `sqrt-pow1` `flip3-+` `associate-*r/` `flip-+`
1×	`cube-mult` `sub-neg` `flip3--` `pow1/2` `pow1/3` `diff-log` `unpow3` `pow-prod-down` `associate-*l/` `sqrt-prod` `flip--` `rem-cbrt-cube` `fma-udef` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

26.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))) (+ (exp x) 1.0)))
2.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series263.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))) (+ (exp x) 1.0)))
41.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	378	824
1	1469	729
2	5001	726

prune290.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes33.0ms

Accuracy

74.4% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.9b

bsearch60.0ms

Steps

Iters	Range		Point
9	-0.04331797882383785	-1.989428328455626e-07	-8.898814212803163e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	36
1	51	36

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6689×	body	10240	exit
382.0ms	12775×	body	80	nan
245.0ms	7444×	body	80	valid
52.0ms	694×	body	160	valid