Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	257×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	5×	body	1280	valid
0.0ms	6×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 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: 15.8b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.7b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series150.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- t x) (- a z))
96.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune204.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 5.0b

Counts

72 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
15.7b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a z))
18.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series186.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (- a z))
50.0ms	(* (- t x) (/ 1 (- a z)))
96.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune231.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	113	12	125

Merged error: 4.8b

Counts

125 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
15.7b	(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
1.0ms	(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

series564.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (- t x))
159.0ms	(cbrt (- t x))
152.0ms	(cbrt (- t x))
94.0ms	(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	196	519
1	449	474
2	1425	457
3	5001	433

prune268.0ms

Filtered

73 candidates to 64 candidates (87.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	72	13	85

Merged error: 4.3b

Counts

85 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.8b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
6.1b	(/ (- y z) (/ (- a z) (- t x)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

9.0ms	(/ (- a z) (- t x))
66.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
17.0ms	(/ (- y z) (/ (- a z) (- t x)))

series544.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- a z) (- t x))
176.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
313.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1035	3079
1	4296	3003
2	5001	3001

prune926.0ms

Filtered

449 candidates to 269 candidates (59.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	439	10	449
Fresh	8	2	10
Picked	1	0	1
Done	2	0	2
Total	450	12	462

Merged error: 2.2b

Counts

462 → 12

regimes519.0ms

Accuracy

10.3% (7.6b remaining)

Error of 11.4b against oracle of 3.8b and baseline of 12.3b

bsearch125.0ms

Steps

Iters	Range	Point
8	1.2719276157137885e+160	1.7714337657579524e+163	1.0048489443141935e+163
7	5.27826461642212e-274	1.0997505507950967e-271	8.482328112026546e-274
8	-1.8630524388761778e+218	-2.530200857107875e+214	-6.340925579506865e+216

Iters

Range

Point

1.2719276157137885e+160

1.7714337657579524e+163

1.0048489443141935e+163

5.27826461642212e-274

1.0997505507950967e-271

8.482328112026546e-274

-1.8630524388761778e+218

-2.530200857107875e+214

-6.340925579506865e+216

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample709.0ms

Algorithm

intervals

Results

262.0ms	7803×	body	80	valid
58.0ms	498×	body	640	valid
40.0ms	269×	body	1280	valid
38.0ms	397×	body	320	valid
15.0ms	254×	body	160	valid
3.0ms	14×	body	2560	valid

Details

sample27.0ms

simplify52.0ms

prune7.0ms

localize8.0ms

rewrite12.0ms

series150.0ms

simplify60.0ms

prune204.0ms

localize10.0ms

rewrite28.0ms

series186.0ms

simplify44.0ms

prune231.0ms

localize17.0ms

rewrite12.0ms

series564.0ms

simplify48.0ms

prune268.0ms

localize9.0ms

rewrite131.0ms

series544.0ms

simplify112.0ms

prune926.0ms

regimes519.0ms

bsearch125.0ms

simplify2.0ms

end0.0ms

sample709.0ms

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