Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	240×	body	80	valid
3.0ms	14×	body	1280	valid
2.0ms	20×	body	320	valid
2.0ms	11×	body	640	valid
0.0ms	2×	body	2560	valid
0.0ms	6×	body	160	valid

simplify55.0ms

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

prune8.0ms

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: 17.1b

Counts

2 → 2

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
17.1b	(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:

9.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series142.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- t x) (- a z))
93.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (51.0ms)

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

prune202.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 7.9b

Counts

72 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.0b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b	(* (- y z) (/ (- t x) (- a z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

9.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series334.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
134.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune307.0ms

Filtered

137 candidates to 95 candidates (69.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	136	13	149

Merged error: 4.4b

Counts

149 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
17.1b	(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))
14.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series175.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
88.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

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

prune255.0ms

Filtered

114 candidates to 72 candidates (63.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	112	15	127

Merged error: 4.4b

Counts

127 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(* (- y z) (/ (- t x) (- a z)))
12.5b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
31×	`associate-r`
26×	`times-frac`
18×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-prod`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
17.0ms	(* (- y z) (/ (- t x) (- a z)))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
175.0ms	(cbrt x)
127.0ms	(* (- y z) (/ (- t x) (- a z)))
158.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (- y z) (/ (- t x) (- a z))))

simplify45.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	363	638
1	1589	575
2	5001	566

prune271.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	6	6	12
Picked	1	0	1
Done	0	2	2
Total	108	13	121

Merged error: 4.4b

Counts

121 → 13

regimes406.0ms

Accuracy

60.1% (3.5b remaining)

Error of 7.1b against oracle of 3.6b and baseline of 12.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40

end0.0ms

sample766.0ms

Algorithm

intervals

Results

309.0ms	7877×	body	80	valid
69.0ms	474×	body	640	valid
47.0ms	270×	body	1280	valid
44.0ms	412×	body	320	valid
17.0ms	242×	body	160	valid
4.0ms	18×	body	2560	valid