Details

sample102.0ms

Algorithm

intervals

Results

28.0ms	58×	body	10240	exit
19.0ms	37×	body	1280	valid
15.0ms	50×	body	640	valid
7.0ms	38×	body	320	valid
7.0ms	117×	body	80	valid
4.0ms	3×	body	2560	valid
3.0ms	78×	body	80	nan
1.0ms	11×	body	160	valid
1.0ms	9×	body	320	nan
1.0ms	6×	body	640	nan
0.0ms	1×	body	1280	nan
0.0ms	2×	body	160	nan

simplify205.0ms

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	1551	7
11	1886	7
12	4545	7
13	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 23.2b

Counts

2 → 1

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)
1.5b	(log (+ (- 1.0 y) (* y (exp z))))
2.8b	(+ (- 1.0 y) (* y (exp z)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
10×	`add-exp-log`
9×	`prod-diff` `add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out`
7×	`log-prod` `associate-l`
5×	`fma-def` `log-pow` `distribute-lft-out--`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `associate-r` `associate-/r*` `flip-+`
2×	`div-sub` `prod-exp` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

9.0ms	(* y (exp z))
22.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
19.0ms	(log (+ (- 1.0 y) (* y (exp z))))
11.0ms	(+ (- 1.0 y) (* y (exp z)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* y (exp z))
154.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
78.0ms	(log (+ (- 1.0 y) (* y (exp z))))
64.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	496	959
1	1999	815
2	5002	791

prune290.0ms

Filtered

123 candidates to 92 candidates (25.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	6	124

Merged error: 4.4b

Counts

124 → 6

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)
2.2b	(log (+ 1.0 (* y (expm1 z))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
63×	`*-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`
5×	`log-prod`
4×	`expm1-log1p-u` `div-sub` `associate-l` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`flip3-+` `fma-neg` `associate-r` `associate-/r*` `flip-+`
2×	`distribute-lft-out` `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 → 143

Calls

4 calls:

9.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
3.0ms	(* y (expm1 z))
8.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
6.0ms	(log (+ 1.0 (* y (expm1 z))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
40.0ms	(* y (expm1 z))
256.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
79.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify87.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	737	2879
1	2731	1989
2	5001	1791

prune293.0ms

Filtered

155 candidates to 89 candidates (42.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	146	9	155
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	149	12	161

Merged error: 4.3b

Counts

161 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
2.2b	(log (+ 1.0 (* y (expm1 z))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

4.0ms	(* y (expm1 z))
11.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(log (+ 1.0 (* y (expm1 z))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* y (expm1 z))
81.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
206.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
79.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify88.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	722	1741
1	3447	1575
2	5001	1482

prune356.0ms

Filtered

184 candidates to 106 candidates (42.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	184	12	196

Merged error: 4.2b

Counts

196 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (/ 1 t) (log (fma (expm1 z) y 1.0))))
0.0b	(fma (expm1 z) y 1.0)
0.1b	(* (/ 1 t) (log (fma (expm1 z) y 1.0)))
2.2b	(log (fma (expm1 z) y 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
75×	`prod-diff`
72×	`add-cube-cbrt`
54×	`associate-l`
46×	`times-frac`
16×	`associate-r`
15×	`log-prod` `unswap-sqr`
14×	`add-exp-log`
11×	`pow1`
9×	`associate-*l/` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--r+` `add-log-exp`
5×	`log-pow` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `*-commutative` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg` `associate-/r` `associate-/l` `distribute-lft-out--`
2×	`div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `frac-2neg` `diff-log` `1-exp` `rem-log-exp` `pow-prod-down` `clear-num` `flip--` `fma-udef`

Counts

4 → 181

Calls

4 calls:

14.0ms	(- x (* (/ 1 t) (log (fma (expm1 z) y 1.0))))
1.0ms	(fma (expm1 z) y 1.0)
8.0ms	(* (/ 1 t) (log (fma (expm1 z) y 1.0)))
2.0ms	(log (fma (expm1 z) y 1.0))

series281.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- x (* (/ 1 t) (log (fma (expm1 z) y 1.0))))
46.0ms	(fma (expm1 z) y 1.0)
86.0ms	(* (/ 1 t) (log (fma (expm1 z) y 1.0)))
71.0ms	(log (fma (expm1 z) y 1.0))

simplify112.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	944	3531
1	3490	2314
2	5001	2168

prune306.0ms

Filtered

193 candidates to 103 candidates (46.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	192	13	205

Merged error: 4.2b

Counts

205 → 13

regimes425.0ms

Accuracy

-3.1% (7.2b remaining)

Error of 11.9b against oracle of 4.6b and baseline of 11.6b

bsearch192.0ms

Steps

Iters	Range		Point
9	4.7151388039762676e-80	1.212700641608673e-73	1.2328997270443114e-76
7	-1.9974011950166226e-147	-7.1959372318129105e-149	-7.878876498544208e-149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	26
1	40	26

end0.0ms

sample3.2s

Algorithm

intervals

Results

790.0ms	1566×	body	10240	exit
750.0ms	1407×	body	1280	valid
477.0ms	1614×	body	640	valid
215.0ms	3486×	body	80	valid
175.0ms	945×	body	320	valid
109.0ms	89×	body	2560	valid
91.0ms	2500×	body	80	nan
57.0ms	489×	body	160	valid
54.0ms	277×	body	640	nan
33.0ms	116×	body	1280	nan
25.0ms	186×	body	320	nan
10.0ms	119×	body	160	nan