Details

sample303.0ms

Algorithm

intervals

Results

16.0ms	411×	body	80	nan
12.0ms	231×	body	80	valid
8.0ms	217×	body	80	overflowed
3.0ms	26×	body	160	valid

simplify76.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.2b

Counts

2 → 1

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))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite56.0ms

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:

11.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
26.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series198.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (42.0ms)

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

prune339.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Merged error: 0.0b

Counts

168 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.1b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.7b	(- (exp (* 2.0 x)) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
9.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
60.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify115.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382

prune566.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	218	4	222

Merged error: 0b

Counts

222 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (* 2.0 x)) 1.0) (* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0))))
0.1b	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
5.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.7b	(- (exp (* 2.0 x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-exp-log`
22×	`add-cube-cbrt`
19×	`times-frac`
18×	`associate-r` `add-cbrt-cube`
9×	`div-exp` `prod-diff`
8×	`prod-exp`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`rec-exp` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `flip--` `div-inv` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip-+` `fma-udef`

Counts

4 → 117

Calls

4 calls:

14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0))))
11.0ms	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0))))
64.0ms	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	545	1394
1	2357	1131
2	5002	1107

prune312.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Merged error: 0b

Counts

133 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
0.1b	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
5.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.7b	(- (exp (* 2.0 x)) 1.0)

rewrite9.0ms

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:

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

series550.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
218.0ms	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	315	802
1	1051	652
2	5001	648

prune214.0ms

Filtered

72 candidates to 54 candidates (75.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	72	4	76

Merged error: 0b

Counts

76 → 4

regimes29.0ms

Accuracy

73.5% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.8b

bsearch15.0ms

Steps

Iters	Range		Point
2	-7.039460350247907e-16	-6.479437596386637e-16	-6.689446129084614e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	17
1	31	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

479.0ms	12291×	body	80	nan
310.0ms	7397×	body	80	valid
248.0ms	6568×	body	80	overflowed
73.0ms	734×	body	160	valid