Details

sample336.0ms

Algorithm

intervals

Results

42.0ms	216×	body	10240	exit
12.0ms	413×	body	80	nan
9.0ms	234×	body	80	valid
2.0ms	26×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2617	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
29×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
15×	`sqrt-div`
10×	`associate-/r` `associate-/l`
8×	`add-log-exp`
6×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
5×	`pow1`
4×	`associate-/r/` `associate-/l/`
2×	`sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `clear-num` `div-inv`
1×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-sub` `div-exp`

Counts

4 → 137

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
13.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series221.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	402	1530
1	1050	1476
2	4194	1460
3	5001	1452

prune303.0ms

Filtered

149 candidates to 102 candidates (31.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Merged error: 0.3b

Counts

150 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (exp (* 2.0 x)))
0.7b	(sqrt (exp (* 2.0 x)))
5.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.7b	(- (exp x) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `sqrt-pow1`
24×	`exp-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

5.0ms	(sqrt (exp (* 2.0 x)))
5.0ms	(sqrt (exp (* 2.0 x)))
9.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series118.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (exp (* 2.0 x)))
23.0ms	(sqrt (exp (* 2.0 x)))
49.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
19.0ms	(- (exp x) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	191	434
1	436	417
2	1166	415
3	3678	413
4	5002	413

prune253.0ms

Filtered

96 candidates to 69 candidates (28.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0.2b

Counts

101 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.7b	(sqrt (exp (* 2.0 x)))
5.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
5.7b	(- (exp x) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`sqrt-pow1`
12×	`exp-prod`
11×	`add-log-exp`
8×	`add-cube-cbrt` `sqrt-prod`
7×	`difference-of-squares`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `rem-sqrt-square` `exp-to-pow` `flip3-+` `pow1/2` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

9.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(sqrt (exp (* 2.0 x)))
9.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series121.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
23.0ms	(sqrt (exp (* 2.0 x)))
31.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	279	482
1	656	454
2	1826	448
3	5002	446

prune235.0ms

Filtered

84 candidates to 61 candidates (27.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0b

Counts

87 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)))))
0.0b	(+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
5.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
5.7b	(- (exp x) 1.0)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

524×	`add-sqr-sqrt`
477×	`times-frac`
418×	`*-un-lft-identity`
329×	`sqrt-prod`
214×	`difference-of-squares`
144×	`add-cube-cbrt`
79×	`distribute-lft-out--`
66×	`associate-/r*`
65×	`sqrt-div`
58×	`distribute-lft-out`
54×	`unpow-prod-down` `sqr-pow`
30×	`associate-/r/`
10×	`add-log-exp`
9×	`associate-/l*`
8×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
3×	`rem-sqrt-square`
2×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+`
1×	`+-commutative` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 370

Calls

4 calls:

55.0ms	(sqrt (/ (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)))))
8.0ms	(+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
9.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series388.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(sqrt (/ (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)))))
25.0ms	(+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
31.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
22.0ms	(- (exp x) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

382 → 382

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1361	10424
1	5001	10295

prune709.0ms

Filtered

382 candidates to 188 candidates (50.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	382	3	385

Merged error: 0b

Counts

385 → 3

regimes31.0ms

Accuracy

99.5% (0.0b remaining)

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

bsearch93.0ms

Steps

Iters	Range		Point
8	9.765870861142247e-20	2.8366563651151703e-16	1.1101738491414888e-16
6	-8.386303929946514e-15	-1.2319365312389687e-15	-3.79195243520061e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	44
1	49	44

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	6626×	body	10240	exit
374.0ms	12421×	body	80	nan
237.0ms	7402×	body	80	valid
54.0ms	724×	body	160	valid