Details

sample110.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
23.0ms	46×	body	10240	exit
13.0ms	47×	body	640	valid
7.0ms	118×	body	80	valid
4.0ms	3×	body	2560	valid
4.0ms	22×	body	320	valid
3.0ms	93×	body	80	nan
2.0ms	7×	body	1280	nan
2.0ms	16×	body	160	valid
1.0ms	5×	body	640	nan
1.0ms	8×	body	320	nan
0.0ms	4×	body	160	nan

simplify221.0ms

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: 23.7b

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)
1.5b	(log (+ (- 1.0 y) (* y (exp z))))
2.0b	(+ (- 1.0 y) (* y (exp z)))

rewrite118.0ms

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:

11.0ms	(* y (exp z))
51.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
19.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
144.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
65.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

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

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

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)))) t)
2.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite33.0ms

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:

5.0ms	(+ 1.0 (* y (expm1 z)))
9.0ms	(* y (expm1 z))
13.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* y (expm1 z)))
34.0ms	(* y (expm1 z))
153.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
67.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (44.0ms)

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

prune297.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize15.0ms

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)
2.7b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.7b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite79.0ms

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:

7.0ms	(* y (expm1 z))
55.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
5.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
5.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* y (expm1 z))
1.8s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
342.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
334.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1209	2979
1	5001	2513

prune599.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))
2.7b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.8b	(log (sqrt (* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))))
2.8b	(log (sqrt (cbrt (+ 1.0 (* y (expm1 z))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `cbrt-div`
24×	`pow1`
19×	`cbrt-prod` `log-prod`
18×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
14×	`flip3-+` `flip-+`
13×	`pow1/3`
12×	`log-div` `sqrt-pow1` `sqrt-div`
10×	`sqrt-prod`
9×	`add-exp-log`
8×	`frac-times`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow1/2` `rem-log-exp`
2×	`pow2` `pow-plus`
1×	`prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 129

Calls

4 calls:

28.0ms	(* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))
5.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
21.0ms	(log (sqrt (* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))))
6.0ms	(log (sqrt (cbrt (+ 1.0 (* y (expm1 z))))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))
331.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
139.0ms	(log (sqrt (* (cbrt (+ 1.0 (* y (expm1 z)))) (cbrt (+ 1.0 (* y (expm1 z)))))))
182.0ms	(log (sqrt (cbrt (+ 1.0 (* y (expm1 z))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1080	2195
1	4381	2030
2	5001	2027

prune699.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

regimes210.0ms

Accuracy

28.2% (5.5b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 11.1b

bsearch88.0ms

Steps

Iters	Range		Point
7	-3.144652509885462e-246	-2.7496425187334983e-248	-3.083544696508266e-246

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	24
1	35	24

end0.0ms

sample3.3s

Algorithm

intervals

Results

769.0ms	1578×	body	10240	exit
758.0ms	1476×	body	1280	valid
435.0ms	1499×	body	640	valid
216.0ms	3611×	body	80	valid
162.0ms	898×	body	320	valid
114.0ms	88×	body	2560	valid
92.0ms	2592×	body	80	nan
53.0ms	470×	body	160	valid
51.0ms	263×	body	640	nan
32.0ms	110×	body	1280	nan
27.0ms	190×	body	320	nan
10.0ms	122×	body	160	nan