Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	257×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	5×	body	1280	valid
0.0ms	6×	body	160	valid

simplify51.0ms

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

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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)

series141.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- t x) (- a z))
90.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (52.0ms)

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

prune189.0ms

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)

rewrite25.0ms

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:

5.0ms	(/ 1 (- a z))
13.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series175.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a z))
49.0ms	(* (- t x) (/ 1 (- a z)))
90.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

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

prune211.0ms

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

localize13.0ms

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)

rewrite14.0ms

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))
5.0ms	(cbrt (- t x))
1.0ms	(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

series530.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- t x))
147.0ms	(cbrt (- t x))
144.0ms	(cbrt (- t x))
90.0ms	(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (39.0ms)

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

prune253.0ms

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)))

rewrite126.0ms

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))
63.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
17.0ms	(/ (- y z) (/ (- a z) (- t x)))

series525.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- a z) (- t x))
173.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
299.0ms	(/ (- 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

prune869.0ms

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

regimes317.0ms

Accuracy

10.3% (7.6b remaining)

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

bsearch131.0ms

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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample779.0ms

Algorithm

intervals

Results

303.0ms	7803×	body	80	valid
77.0ms	498×	body	640	valid
48.0ms	269×	body	1280	valid
46.0ms	397×	body	320	valid
19.0ms	254×	body	160	valid
5.0ms	14×	body	2560	valid