Details

sample107.0ms

Algorithm

intervals

Results

22.0ms	43×	body	10240	exit
21.0ms	40×	body	1280	valid
18.0ms	60×	body	640	valid
11.0ms	8×	body	2560	valid
6.0ms	104×	body	80	valid
5.0ms	32×	body	320	valid
3.0ms	87×	body	80	nan
2.0ms	14×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	2×	body	1280	nan
0.0ms	3×	body	320	nan
0.0ms	1×	body	160	nan

simplify217.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 28.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.8b	(log (+ (- 1.0 y) (* y (exp z))))
2.3b	(+ (- 1.0 y) (* y (exp z)))

rewrite32.0ms

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))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))
11.0ms	(+ (- 1.0 y) (* y (exp z)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
194.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
75.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

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

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
4.3b	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
18.4b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `flip3--` `pow1/3` `flip--` `distribute-lft-out--`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`log-prod`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 99

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
11.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
1.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
1.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (- 1.0 y))
106.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
257.0ms	(log (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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	517	1081
1	1755	983
2	5002	917

prune438.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
0.3b	(expm1 (log1p (log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))))
4.3b	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
18.4b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`cbrt-prod`
27×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow1` `cbrt-div`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
7×	`add-exp-log`
6×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`log-prod`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `expm1-log1p` `pow-plus` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef`

Counts

4 → 93

Calls

4 calls:

11.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
1.0ms	(expm1 (log1p (log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))))
1.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
1.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
821.0ms	(expm1 (log1p (log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))))
260.0ms	(log (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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	629	1306
1	2357	1179
2	5001	1124

prune465.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

4.7b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.9b	(/ (* z y) t)
6.2b	(/ (* (pow z 2) y) t)
8.1b	(* (pow z 2) y)

rewrite18.0ms

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:

1.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)
5.0ms	(/ (* (pow z 2) y) t)
5.0ms	(* (pow z 2) y)

series151.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
23.0ms	(/ (* z y) t)
18.0ms	(/ (* (pow z 2) y) t)
17.0ms	(* (pow z 2) y)

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	479
1	1407	406
2	5001	406

prune506.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.4b

regimes780.0ms

Accuracy

72.9% (4.6b remaining)

Error of 8.5b against oracle of 3.9b and baseline of 20.9b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample3.1s

Algorithm

intervals

Results

774.0ms	1573×	body	10240	exit
729.0ms	1401×	body	1280	valid
456.0ms	1534×	body	640	valid
209.0ms	3560×	body	80	valid
174.0ms	952×	body	320	valid
125.0ms	99×	body	2560	valid
90.0ms	2446×	body	80	nan
57.0ms	479×	body	160	valid
52.0ms	262×	body	640	nan
31.0ms	106×	body	1280	nan
23.0ms	175×	body	320	nan
11.0ms	124×	body	160	nan