Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	250×	body	80	valid
4.0ms	14×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	3×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
4.0b	(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)

series180.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y z) (- a z))
125.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

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

prune225.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.8b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite35.0ms

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))
25.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series220.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a z))
55.0ms	(* (- y z) (/ 1 (- a z)))
127.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	340	602
1	1472	525
2	5002	481

prune296.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
4.0b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite19.0ms

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:

15.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series180.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y z) (- a z))
127.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify77.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (66.0ms)

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

prune193.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
8.2b	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

rewrite9.0ms

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:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
0.0ms	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

series646.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (- a z))
173.0ms	(cbrt (- a z))
167.0ms	(cbrt (- a z))
137.0ms	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	203	532
1	492	489
2	1845	471
3	5003	446

prune328.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.1b

regimes291.0ms

Accuracy

19.2% (6.6b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 11.6b

bsearch109.0ms

Steps

Iters	Range		Point
9	2.46683021584194e+172	5.582883325981149e+180	1.3098447934604612e+176
9	-3.1520536883671544e+112	-3.662546024879469e+104	-3.102526111378278e+112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample711.0ms

Algorithm

intervals

Results

266.0ms	7795×	body	80	valid
54.0ms	460×	body	640	valid
41.0ms	255×	body	1280	valid
39.0ms	434×	body	320	valid
20.0ms	280×	body	160	valid
3.0ms	14×	body	2560	valid