Details

sample100.0ms

Algorithm

intervals

Results

24.0ms	46×	body	1280	valid
19.0ms	39×	body	10240	exit
12.0ms	44×	body	640	valid
9.0ms	5×	body	2560	valid
7.0ms	120×	body	80	valid
5.0ms	28×	body	320	valid
2.0ms	67×	body	80	nan
2.0ms	16×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	5×	body	1280	nan
0.0ms	3×	body	320	nan
0.0ms	3×	body	160	nan

simplify212.0ms

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: 25.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
3.0b	(+ (- 1.0 y) (* y (exp z)))
3.0b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite29.0ms

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)
7.0ms	(+ (- 1.0 y) (* y (exp z)))
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
146.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
33.0ms	(+ (- 1.0 y) (* y (exp z)))
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

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

prune332.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 5.9b

Counts

115 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* y (expm1 z)))
0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
5.1b	(log (+ 1.0 (* y (expm1 z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

3.0ms	(+ 1.0 (* y (expm1 z)))
3.0ms	(* y (expm1 z))
5.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ 1.0 (* y (expm1 z)))
35.0ms	(* y (expm1 z))
151.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	473	718
1	1893	652
2	5001	644

prune276.0ms

Filtered

99 candidates to 78 candidates (78.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 5.9b

Counts

104 → 8

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))
5.1b	(log (+ 1.0 (* y (expm1 z))))

rewrite20.0ms

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:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ 1.0 (* y (expm1 z)))
36.0ms	(* y (expm1 z))
155.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify64.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (56.0ms)

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

prune276.0ms

Filtered

103 candidates to 81 candidates (78.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Merged error: 5.9b

Counts

111 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
5.1b	(log (+ 1.0 (* y (expm1 z))))

rewrite22.0ms

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:

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

series406.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* y (expm1 z))
200.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
79.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify95.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (74.0ms)

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

prune330.0ms

Filtered

171 candidates to 102 candidates (59.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	169	10	179

Merged error: 5.9b

Counts

179 → 10

regimes314.0ms

Accuracy

8.6% (6.7b remaining)

Error of 11.1b against oracle of 4.4b and baseline of 11.8b

bsearch426.0ms

Steps

Iters	Range		Point
9	1.2573898009304202e+60	3.5147876040828643e+68	3.455676482898611e+68
10	0.4751518629468822	14896478692.168556	0.509833754303126
10	-1.7786299918085942e-77	-3.7513271124353733e-87	-2.3371547418121854e-79
9	-10692105538175.213	-83862155.37710363	-2045829589.788266

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	50
1	55	50

end0.0ms

sample3.1s

Algorithm

intervals

Results

758.0ms	1426×	body	1280	valid
742.0ms	1497×	body	10240	exit
469.0ms	1622×	body	640	valid
217.0ms	3526×	body	80	valid
173.0ms	927×	body	320	valid
92.0ms	2450×	body	80	nan
85.0ms	71×	body	2560	valid
54.0ms	273×	body	640	nan
51.0ms	459×	body	160	valid
36.0ms	109×	body	1280	nan
24.0ms	182×	body	320	nan
10.0ms	117×	body	160	nan