Details

sample334.0ms

Algorithm

intervals

Results

29.0ms	407×	body	80	nan
21.0ms	240×	body	80	valid
15.0ms	220×	body	80	overflowed
3.0ms	19×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite58.0ms

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)))
17.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

series210.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

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

prune398.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.0b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0b	(- (exp (* 2.0 x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

9.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	361	673
1	1258	564
2	5002	559

prune286.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (+ (exp x) 1.0)))
0.1b	(log1p (+ (exp x) 1.0))
4.0b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0b	(- (exp (* 2.0 x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(expm1 (log1p (+ (exp x) 1.0)))
0.0ms	(log1p (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series255.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(expm1 (log1p (+ (exp x) 1.0)))
72.0ms	(log1p (+ (exp x) 1.0))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify109.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	266	460
1	819	351
2	3757	340
3	5001	325

prune259.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp x))
0.0b	(* (cbrt (exp x)) (cbrt (exp x)))
4.0b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0b	(- (exp (* 2.0 x)) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`cbrt-prod`
11×	`pow1`
9×	`prod-diff`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (exp x))
7.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series249.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (exp x))
101.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify166.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	289	659
1	923	542
2	4806	504
3	5001	489

prune346.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

74.6% (0.7b remaining)

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

bsearch47.0ms

Steps

Iters	Range		Point
7	-5.023588783947765e-05	-7.23934040408857e-07	-1.4851276610030483e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	22
1	28	22

end0.0ms

sample2.4s

Algorithm

intervals

Results

909.0ms	12822×	body	80	nan
574.0ms	7450×	body	80	valid
465.0ms	6743×	body	80	overflowed
106.0ms	691×	body	160	valid