Details

sample92.0ms

Algorithm

intervals

Results

29.0ms	53×	body	1280	valid
10.0ms	34×	body	640	valid
8.0ms	135×	body	80	valid
7.0ms	88×	body	80	overflowed
5.0ms	3×	body	2560	valid
4.0ms	21×	body	320	valid
3.0ms	15×	body	640	nan
3.0ms	87×	body	80	nan
1.0ms	13×	body	160	valid
1.0ms	7×	body	320	nan
1.0ms	3×	body	1280	nan
1.0ms	6×	body	160	nan

simplify214.0ms

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: 21.2b

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)
1.5b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite54.0ms

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))
23.0ms	(/ (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)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
148.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
71.0ms	(log (+ (- 1.0 y) (* y (exp z))))
34.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

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

prune368.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.8b	(log (+ 1.0 (* y (expm1 z))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
20×	`pow1`
14×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `flip3-+` `fma-neg` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate--r-` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

3.0ms	(* y (expm1 z))
9.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* y (expm1 z))
78.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
150.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
70.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify82.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	746	2869
1	2769	1983
2	5001	1785

prune330.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (expm1 (log1p (* y (expm1 z)))))) t)
1.1b	(expm1 (log1p (* y (expm1 z))))
3.8b	(log (+ 1.0 (expm1 (log1p (* y (expm1 z))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

3.0ms	(* y (expm1 z))
7.0ms	(/ (log (+ 1.0 (expm1 (log1p (* y (expm1 z)))))) t)
0.0ms	(expm1 (log1p (* y (expm1 z))))
2.0ms	(log (+ 1.0 (expm1 (log1p (* y (expm1 z))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (expm1 z))
194.0ms	(/ (log (+ 1.0 (expm1 (log1p (* y (expm1 z)))))) t)
108.0ms	(expm1 (log1p (* y (expm1 z))))
105.0ms	(log (+ 1.0 (expm1 (log1p (* y (expm1 z))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	454	876
1	1709	794
2	5002	757

prune339.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
3.9b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.9b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-div`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `log-div` `flip3-+` `pow1/3` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
164.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
152.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
148.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	318	880
1	1062	820
2	5001	794

prune390.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.6b

regimes202.0ms

Accuracy

42.2% (4.4b remaining)

Error of 5.8b against oracle of 1.5b and baseline of 9.0b

bsearch166.0ms

Steps

Iters	Range		Point
10	7.800223637927871e-45	1.6335448673401457e-32	1.8293353697925934e-33
8	-0.6196216933291611	-0.0001027795604175201	-0.00031198126899025023

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	32
1	45	32

end0.0ms

sample2.5s

Algorithm

intervals

Results

730.0ms	1357×	body	1280	valid
440.0ms	1456×	body	640	valid
245.0ms	3931×	body	80	valid
144.0ms	784×	body	320	valid
131.0ms	100×	body	2560	valid
130.0ms	2487×	body	80	overflowed
108.0ms	2696×	body	80	nan
61.0ms	277×	body	640	nan
45.0ms	399×	body	160	valid
35.0ms	114×	body	1280	nan
27.0ms	199×	body	320	nan
10.0ms	116×	body	160	nan