Details

sample138.0ms

Algorithm

intervals

Results

28.0ms	43×	body	10240	exit
23.0ms	52×	body	640	valid
22.0ms	37×	body	1280	valid
15.0ms	124×	body	80	valid
9.0ms	23×	body	320	valid
6.0ms	87×	body	80	nan
5.0ms	17×	body	640	nan
3.0ms	19×	body	160	valid
3.0ms	8×	body	1280	nan
3.0ms	1×	body	2560	valid
2.0ms	8×	body	320	nan

simplify222.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
3.7b	(+ (- 1.0 y) (* y (exp z)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
22.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
8.0ms	(log (+ (- 1.0 y) (* y (exp z))))
15.0ms	(+ (- 1.0 y) (* y (exp z)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
146.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
72.0ms	(log (+ (- 1.0 y) (* y (exp z))))
33.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune348.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 y))
0.3b	(cbrt (- 1.0 y))
4.5b	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
14.6b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
7×	`add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`rem-log-exp` `log-pow` `fma-udef`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (- 1.0 y))
2.0ms	(cbrt (- 1.0 y))
1.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
0.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (- 1.0 y))
95.0ms	(cbrt (- 1.0 y))
256.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
193.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	394	743
1	1256	663
2	5001	637

prune312.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

localize24.0ms

Local error

Found 4 expressions with local error:

4.5b	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
14.6b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
14.6b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
14.6b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `fma-udef`
1×	`rem-log-exp` `log-pow`

Counts

4 → 44

Calls

4 calls:

1.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
0.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
0.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
0.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

series868.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
206.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
204.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))
200.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

simplify116.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	250	829
1	836	703
2	3884	682
3	5001	632

prune338.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.1b	(/ (* z y) t)
6.2b	(/ (* (pow z 2) y) t)
8.3b	(* (pow z 2) y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
3.0ms	(/ (* z y) t)
4.0ms	(/ (* (pow z 2) y) t)
6.0ms	(* (pow z 2) y)

series150.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
19.0ms	(/ (* z y) t)
19.0ms	(/ (* (pow z 2) y) t)
18.0ms	(* (pow z 2) y)

simplify54.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	300	473
1	1353	406
2	5002	406

prune308.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

regimes671.0ms

Accuracy

72.3% (4.8b remaining)

Error of 8.6b against oracle of 3.8b and baseline of 21.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

806.0ms	1379×	body	1280	valid
800.0ms	1463×	body	10240	exit
545.0ms	1607×	body	640	valid
359.0ms	3529×	body	80	valid
213.0ms	945×	body	320	valid
160.0ms	2510×	body	80	nan
110.0ms	82×	body	2560	valid
79.0ms	485×	body	160	valid
73.0ms	291×	body	640	nan
39.0ms	118×	body	1280	nan
32.0ms	193×	body	320	nan
12.0ms	104×	body	160	nan