Details

sample115.0ms

Algorithm

intervals

Results

39.0ms	53×	body	1280	valid
17.0ms	40×	body	640	valid
11.0ms	122×	body	80	valid
8.0ms	5×	body	2560	valid
7.0ms	25×	body	320	valid
5.0ms	85×	body	80	nan
3.0ms	45×	body	80	overflowed
3.0ms	9×	body	640	nan
2.0ms	12×	body	160	valid
2.0ms	4×	body	1280	nan
1.0ms	3×	body	320	nan
1.0ms	4×	body	160	nan

simplify218.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

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)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
2.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite57.0ms

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))
25.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
152.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
75.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series256.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* y (expm1 z))
149.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	429	631
1	1711	580
2	5002	571

prune261.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (log (+ 1.0 (* y (expm1 z)))) t))
2.9b	(log (+ 1.0 (* y (expm1 z))))
2.9b	(log (+ 1.0 (* y (expm1 z))))
2.9b	(log (+ 1.0 (* y (expm1 z))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 75

Calls

4 calls:

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

series822.0ms

Counts

4 → 12

Calls

4 calls:

607.0ms	(cbrt (/ (log (+ 1.0 (* y (expm1 z)))) t))
73.0ms	(log (+ 1.0 (* y (expm1 z))))
74.0ms	(log (+ 1.0 (* y (expm1 z))))
68.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	499	997
1	1768	926
2	5001	917

prune446.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (+ 1.0 (* y (expm1 z))))
2.9b	(log (+ 1.0 (* y (expm1 z))))
2.9b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
2.9b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `log-div`
6×	`cbrt-prod` `log-pow`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `rem-log-exp` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 72

Calls

4 calls:

2.0ms	(log (+ 1.0 (* y (expm1 z))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))
2.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(log (+ 1.0 (* y (expm1 z))))
68.0ms	(log (+ 1.0 (* y (expm1 z))))
141.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
141.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	305	800
1	1000	724
2	4884	702
3	5001	702

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes342.0ms

Accuracy

33% (4.6b remaining)

Error of 9.2b against oracle of 4.6b and baseline of 11.5b

bsearch221.0ms

Steps

Iters	Range		Point
7	2.764917254205367e-55	9.76618566742562e-54	6.291107488971322e-55
8	5.372578135583532e-175	4.22161995161178e-172	1.542824074531081e-172
6	-1.0593086886337258e-08	-1.856415563400247e-09	-3.016368863520559e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	39	32
1	42	16
2	45	16
3	45	16

end0.0ms

sample3.3s

Algorithm

intervals

Results

975.0ms	1432×	body	1280	valid
675.0ms	1657×	body	640	valid
314.0ms	3477×	body	80	valid
241.0ms	899×	body	320	valid
156.0ms	2529×	body	80	nan
133.0ms	89×	body	2560	valid
107.0ms	1544×	body	80	overflowed
96.0ms	306×	body	640	nan
83.0ms	482×	body	160	valid
51.0ms	117×	body	1280	nan
39.0ms	181×	body	320	nan
18.0ms	116×	body	160	nan