Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	52×	body	1280	valid
20.0ms	43×	body	10240	exit
12.0ms	44×	body	640	valid
6.0ms	112×	body	80	valid
5.0ms	28×	body	320	valid
3.0ms	85×	body	80	nan
3.0ms	2×	body	2560	valid
2.0ms	12×	body	640	nan
2.0ms	19×	body	160	valid
1.0ms	4×	body	1280	nan
1.0ms	7×	body	320	nan
0.0ms	2×	body	160	nan

simplify213.0ms

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: 27.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.8b	(log (+ (- 1.0 y) (* y (exp z))))
4.1b	(+ (- 1.0 y) (* y (exp z)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

56.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
21.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 1.0 y) (* y (exp z)))

series274.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
76.0ms	(log (+ (- 1.0 y) (* y (exp z))))
38.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	450	843
1	1824	715
2	5002	691

prune343.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 3 expressions with local error:

3.0b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
7.7b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
8.6b	(* (pow z 2) y)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`associate-l`
7×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-r` `prod-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
12.0ms	(* (pow z 2) y)

series174.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
94.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
18.0ms	(* (pow z 2) y)

simplify145.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	227	586
1	791	528
2	4529	528
3	5001	524

prune293.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))))
3.0b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
7.6b	(/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))))
8.6b	(* (pow z 2) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
16×	`associate-/r*`
13×	`add-cbrt-cube`
8×	`div-exp` `associate-l`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-flip` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `inv-pow`

Counts

4 → 146

Calls

4 calls:

10.0ms	(/ 1 (/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))))
0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
7.0ms	(/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))))
12.0ms	(* (pow z 2) y)

series412.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))))
65.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
179.0ms	(/ t (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))))
19.0ms	(* (pow z 2) y)

simplify69.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	520	1785
1	2625	1634
2	5002	1547

prune475.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (pow z 2) y)
18.0b	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
18.0b	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
18.0b	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
34×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`add-exp-log`
8×	`associate-l`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-div` `pow1/3` `associate-r` `prod-exp` `div-inv`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

12.0ms	(* (pow z 2) y)
2.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
5.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
3.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))

series946.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (pow z 2) y)
309.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
308.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
309.0ms	(cbrt (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	339	1572
1	1050	1474
2	5001	1459

prune580.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

regimes671.0ms

Accuracy

74.6% (4.1b remaining)

Error of 8.8b against oracle of 4.7b and baseline of 20.9b

bsearch146.0ms

Steps

Iters	Range		Point
8	2.6474833247400647e-96	1.762045633081938e-93	4.549364555403628e-95
8	-8.744032506619758	-0.007402571928667657	-0.012438934411162209

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	42
1	46	42

end0.0ms

sample3.2s

Algorithm

intervals

Results

778.0ms	1506×	body	1280	valid
758.0ms	1549×	body	10240	exit
432.0ms	1541×	body	640	valid
209.0ms	3504×	body	80	valid
161.0ms	920×	body	320	valid
97.0ms	73×	body	2560	valid
87.0ms	2515×	body	80	nan
53.0ms	491×	body	160	valid
51.0ms	267×	body	640	nan
33.0ms	114×	body	1280	nan
23.0ms	184×	body	320	nan
11.0ms	99×	body	160	nan