Details

sample123.0ms

Algorithm

intervals

Results

33.0ms	48×	body	1280	valid
23.0ms	45×	body	10240	exit
17.0ms	56×	body	640	valid
7.0ms	115×	body	80	valid
6.0ms	25×	body	320	valid
5.0ms	2×	body	2560	valid
4.0ms	96×	body	80	nan
2.0ms	9×	body	640	nan
1.0ms	4×	body	1280	nan
1.0ms	11×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	6×	body	160	nan

simplify209.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 23.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.3b	(log (+ (- 1.0 y) (* y (exp z))))
3.2b	(+ (- 1.0 y) (* y (exp z)))

rewrite28.0ms

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))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
156.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))
38.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

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

prune319.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	10	115

Merged error: 4.6b

Counts

115 → 10

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)
2.4b	(log (+ 1.0 (* y (expm1 z))))

rewrite25.0ms

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))
5.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
36.0ms	(* y (expm1 z))
156.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
73.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify90.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (64.0ms)

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

prune331.0ms

Filtered

153 candidates to 89 candidates (58.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	144	9	153
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	151	12	163

Merged error: 4.6b

Counts

163 → 12

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))
2.4b	(log (+ 1.0 (* y (expm1 z))))

rewrite20.0ms

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:

3.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
4.0ms	(* y (expm1 z))
8.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
36.0ms	(* y (expm1 z))
154.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify65.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (55.0ms)

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

prune272.0ms

Filtered

107 candidates to 82 candidates (76.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	108	11	119

Merged error: 4.6b

Counts

119 → 11

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)))))
2.4b	(log (+ 1.0 (* y (expm1 z))))

rewrite21.0ms

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

series385.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* y (expm1 z))
77.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
199.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
74.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify89.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5001	1448

prune299.0ms

Filtered

171 candidates to 102 candidates (59.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	171	11	182

Merged error: 4.5b

Counts

182 → 11

regimes450.0ms

Accuracy

41.6% (4.2b remaining)

Error of 8.8b against oracle of 4.6b and baseline of 11.7b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample3.1s

Algorithm

intervals

Results

781.0ms	1456×	body	1280	valid
752.0ms	1479×	body	10240	exit
469.0ms	1596×	body	640	valid
222.0ms	3539×	body	80	valid
170.0ms	917×	body	320	valid
106.0ms	80×	body	2560	valid
95.0ms	2503×	body	80	nan
51.0ms	439×	body	160	valid
48.0ms	242×	body	640	nan
32.0ms	105×	body	1280	nan
25.0ms	188×	body	320	nan
10.0ms	115×	body	160	nan