Details

sample119.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
26.0ms	57×	body	640	valid
9.0ms	101×	body	80	valid
9.0ms	32×	body	320	valid
6.0ms	91×	body	80	nan
5.0ms	3×	body	2560	valid
4.0ms	14×	body	640	nan
4.0ms	51×	body	80	overflowed
3.0ms	16×	body	160	valid
2.0ms	10×	body	320	nan
2.0ms	4×	body	1280	nan
1.0ms	4×	body	160	nan

simplify220.0ms

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: 25.9b

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)
1.0b	(log (+ (- 1.0 y) (* y (exp z))))
3.1b	(+ (- 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)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
151.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
72.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 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

prune373.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite26.0ms

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:

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

series353.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
37.0ms	(* y (expm1 z))
158.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
78.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify81.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (61.0ms)

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

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
2.5b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.5b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 189

Calls

4 calls:

3.0ms	(* y (expm1 z))
29.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* y (expm1 z))
1.6s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
335.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
338.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1209	2963
1	5001	2509

prune617.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
0.0b	(* y (expm1 z))
0.1b	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
2.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`add-exp-log` `associate-r`
11×	`times-frac` `add-cbrt-cube`
10×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-neg` `prod-diff` `cbrt-unprod`
2×	`log-div` `div-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `flip3-+` `diff-log` `1-exp` `associate-*r/` `rem-log-exp` `un-div-inv` `flip--` `flip-+` `div-inv`

Counts

4 → 95

Calls

4 calls:

6.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
3.0ms	(* y (expm1 z))
9.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
37.0ms	(* y (expm1 z))
157.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
70.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify68.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	598	881
1	2528	770
2	5001	730

prune323.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

regimes217.0ms

Accuracy

35.1% (5.0b remaining)

Error of 8.7b against oracle of 3.7b and baseline of 11.4b

bsearch163.0ms

Steps

Iters	Range		Point
8	7.828017428086319e-118	4.340545787691401e-113	7.618234992760663e-115
6	-7.651541911375171e-102	-5.255445760343639e-103	-7.434217587337029e-102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	14
1	32	14

end0.0ms

sample3.2s

Algorithm

intervals

Results

993.0ms	1477×	body	1280	valid
594.0ms	1474×	body	640	valid
318.0ms	3572×	body	80	valid
260.0ms	961×	body	320	valid
152.0ms	2452×	body	80	nan
109.0ms	1512×	body	80	overflowed
107.0ms	74×	body	2560	valid
81.0ms	268×	body	640	nan
80.0ms	465×	body	160	valid
47.0ms	210×	body	320	nan
46.0ms	107×	body	1280	nan
14.0ms	103×	body	160	nan