Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	254×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	7×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.0b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite15.0ms

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:

12.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series163.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- y z) (- a z))
116.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune218.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.6b	(* (/ (- y z) (- a z)) (- t x))
1.7b	(+ (* (/ (- y z) (- a z)) (- t x)) x)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

12.0ms	(/ (- y z) (- a z))
38.0ms	(* (/ (- y z) (- a z)) (- t x))
14.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

series537.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- y z) (- a z))
313.0ms	(* (/ (- y z) (- a z)) (- t x))
177.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	682	1497
1	2657	1254
2	5002	1252

prune438.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t x))
0.6b	(* (cbrt (- t x)) (cbrt (- t x)))
1.6b	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
8.0b	(+ (* (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x))) x)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
39×	`associate-l`
38×	`cbrt-div`
33×	`cbrt-prod`
26×	`times-frac`
24×	`add-cube-cbrt`
20×	`frac-times` `flip3--` `flip--`
18×	`add-exp-log`
17×	`distribute-lft-out--`
16×	`pow1`
15×	`difference-of-squares`
14×	`associate-*r/`
12×	`add-cbrt-cube`
10×	`swap-sqr`
9×	`associate-r`
7×	`pow1/3` `associate-*l/` `prod-exp` `cbrt-unprod`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sum-log` `flip-+` `div-inv`

Counts

4 → 160

Calls

4 calls:

2.0ms	(cbrt (- t x))
20.0ms	(* (cbrt (- t x)) (cbrt (- t x)))
48.0ms	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
111.0ms	(+ (* (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x))) x)

series654.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- t x))
131.0ms	(* (cbrt (- t x)) (cbrt (- t x)))
195.0ms	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
177.0ms	(+ (* (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x))) x)

simplify90.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	712	1717
1	2802	1552
2	5002	1476

prune563.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t x))
0.6b	(* (cbrt (- t x)) (cbrt (- t x)))
1.6b	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
10.2b	(fma (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x)) x)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
39×	`associate-l`
38×	`cbrt-div`
33×	`cbrt-prod`
26×	`times-frac`
24×	`add-cube-cbrt`
20×	`frac-times` `flip3--` `flip--`
18×	`add-exp-log`
17×	`distribute-lft-out--`
16×	`pow1`
15×	`difference-of-squares`
14×	`associate-*r/`
12×	`add-cbrt-cube`
10×	`swap-sqr`
9×	`associate-r`
7×	`pow1/3` `associate-*l/` `prod-exp` `cbrt-unprod`
6×	`unswap-sqr`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus` `fma-udef` `div-inv`

Counts

4 → 156

Calls

4 calls:

2.0ms	(cbrt (- t x))
20.0ms	(* (cbrt (- t x)) (cbrt (- t x)))
50.0ms	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
0.0ms	(fma (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x)) x)

series744.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- t x))
134.0ms	(* (cbrt (- t x)) (cbrt (- t x)))
198.0ms	(* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x))))
264.0ms	(fma (* (/ (- y z) (- a z)) (* (cbrt (- t x)) (cbrt (- t x)))) (cbrt (- t x)) x)

simplify77.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	645	1602
1	2493	1468
2	5001	1403

prune505.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.3b

regimes438.0ms

Accuracy

15.4% (7.0b remaining)

Error of 10.4b against oracle of 3.3b and baseline of 11.7b

bsearch65.0ms

Steps

Iters	Range		Point
6	4.908917336260006e-217	2.4894908659714922e-216	8.589346470906942e-217
5	-9.392129705024728e-39	-2.6876800658575546e-39	-2.728290819567779e-39

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample958.0ms

Algorithm

intervals

Results

455.0ms	7811×	body	80	valid
75.0ms	466×	body	640	valid
60.0ms	287×	body	1280	valid
52.0ms	402×	body	320	valid
26.0ms	286×	body	160	valid
3.0ms	13×	body	2560	valid