Details

sample109.0ms

Algorithm

intervals

Results

33.0ms	47×	body	1280	valid
20.0ms	49×	body	640	valid
10.0ms	111×	body	80	valid
7.0ms	27×	body	320	valid
6.0ms	97×	body	80	nan
4.0ms	59×	body	80	overflowed
4.0ms	22×	body	160	valid
2.0ms	6×	body	1280	nan
2.0ms	5×	body	640	nan
1.0ms	6×	body	320	nan
1.0ms	8×	body	160	nan

simplify214.0ms

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: 26.5b

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)
2.2b	(log (+ (- 1.0 y) (* y (exp z))))
3.8b	(+ (- 1.0 y) (* y (exp z)))

rewrite56.0ms

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))
24.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
152.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))
34.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

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

prune374.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series267.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* y (expm1 z))
156.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
74.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	429	631
1	1711	580
2	5002	571

prune258.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
67×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow1`
20×	`add-exp-log` `associate-/r*`
17×	`log-pow`
13×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

3.0ms	(* y (expm1 z))
2.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* y (expm1 z))
205.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
81.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify87.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5002	1448

prune418.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.1b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.4b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.4b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
80×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
32×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
12×	`log-prod`
10×	`sqrt-div`
9×	`sqrt-prod`
8×	`add-exp-log` `log-div` `distribute-lft1-in` `distribute-rgt1-in`
6×	`flip3-+` `add-cbrt-cube` `flip-+`
4×	`expm1-log1p-u` `count-2` `div-sub` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`associate-+l-` `associate-+r-` `rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 186

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
28.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

352.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.5s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
342.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
343.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1260	3109
1	5002	2589

prune603.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.2b

regimes290.0ms

Accuracy

39.6% (4.5b remaining)

Error of 8.2b against oracle of 3.7b and baseline of 11.2b

bsearch153.0ms

Steps

Iters	Range		Point
8	4.120859846406049e-58	2.66572929097632e-55	4.717741906354947e-57
5	-5.111952297160968e-38	-2.2868282571572898e-38	-4.6972541441660704e-38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	38
1	47	38

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	1489×	body	1280	valid
634.0ms	1525×	body	640	valid
324.0ms	3565×	body	80	valid
249.0ms	903×	body	320	valid
168.0ms	2551×	body	80	nan
106.0ms	1490×	body	80	overflowed
102.0ms	69×	body	2560	valid
87.0ms	264×	body	640	nan
84.0ms	473×	body	160	valid
58.0ms	134×	body	1280	nan
39.0ms	176×	body	320	nan
14.0ms	97×	body	160	nan