Details

sample112.0ms

Algorithm

intervals

Results

27.0ms	52×	body	10240	exit
27.0ms	49×	body	1280	valid
15.0ms	51×	body	640	valid
7.0ms	108×	body	80	valid
6.0ms	34×	body	320	valid
4.0ms	3×	body	2560	valid
3.0ms	86×	body	80	nan
2.0ms	5×	body	1280	nan
1.0ms	7×	body	640	nan
1.0ms	11×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	4×	body	160	nan

simplify219.0ms

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: 27.0b

localize13.0ms

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	(+ (- 1.0 y) (* y (exp z)))
3.0b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite58.0ms

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)
17.0ms	(+ (- 1.0 y) (* y (exp z)))
10.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* y (exp z))
148.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
38.0ms	(+ (- 1.0 y) (* y (exp z)))
74.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (53.0ms)

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

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

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)
4.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite27.0ms

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:

10.0ms	(- 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))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
36.0ms	(* y (expm1 z))
153.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
73.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify78.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (58.0ms)

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

prune376.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.3b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
4.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite23.0ms

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))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (expm1 z))
197.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
79.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
70.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify83.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (68.0ms)

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

prune629.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* y (expm1 z)))
0.0b	(* y (expm1 z))
0.1b	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
4.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`add-exp-log` `add-cube-cbrt` `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-def` `cbrt-unprod`
2×	`log-div` `flip3-+` `div-exp` `pow-prod-down` `log-pow` `*-commutative` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-*r/` `rem-log-exp` `sum-log` `un-div-inv` `div-inv`

Counts

4 → 91

Calls

4 calls:

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

series290.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ 1.0 (* y (expm1 z)))
35.0ms	(* y (expm1 z))
149.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify60.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	561	719
1	2448	623
2	5001	589

prune282.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.2b

regimes422.0ms

Accuracy

15.1% (5.8b remaining)

Error of 10.2b against oracle of 4.4b and baseline of 11.2b

bsearch413.0ms

Steps

Iters	Range		Point
8	4.2323725200470647e+114	1.248238243448428e+117	4.866686842255615e+116
8	0.004380743253548005	7.474768614521862	0.00692258192467828
8	-2.410461602610409e-243	-3.6841099953537603e-246	-4.7416200176225476e-244
8	-1.7226588805599507e+62	-3.8658731844659564e+59	-4.057697116478604e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	60
1	86	60

end0.0ms

sample3.3s

Algorithm

intervals

Results

804.0ms	1556×	body	10240	exit
767.0ms	1406×	body	1280	valid
498.0ms	1617×	body	640	valid
226.0ms	3542×	body	80	valid
188.0ms	938×	body	320	valid
103.0ms	82×	body	2560	valid
97.0ms	2456×	body	80	nan
53.0ms	254×	body	640	nan
53.0ms	456×	body	160	valid
36.0ms	117×	body	1280	nan
32.0ms	225×	body	320	nan
11.0ms	101×	body	160	nan