Details

sample105.0ms

Algorithm

intervals

Results

24.0ms	51×	body	10240	exit
23.0ms	43×	body	1280	valid
17.0ms	52×	body	640	valid
7.0ms	114×	body	80	valid
5.0ms	29×	body	320	valid
3.0ms	99×	body	80	nan
2.0ms	1×	body	2560	valid
2.0ms	11×	body	640	nan
2.0ms	18×	body	160	valid
1.0ms	7×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	2×	body	160	nan

simplify208.0ms

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: 25.7b

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)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
3.6b	(+ (- 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))
22.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
11.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
155.0ms	(/ (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)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

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

prune365.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.4b	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`prod-diff` `add-log-exp`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log` `fma-def`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
2×	`log-div` `flip3-+` `pow1/3` `sum-log` `flip-+`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `log-pow` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
15.0ms	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
34.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt y)
173.0ms	(cbrt y)
87.0ms	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
52.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	328	776
1	1375	565
2	5002	504

prune324.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt` `associate-+l+`
18×	`prod-diff`
14×	`add-log-exp`
12×	`log-prod`
10×	`fma-def`
6×	`pow1` `add-exp-log` `cbrt-prod`
4×	`expm1-log1p-u` `log-div` `cbrt-div` `flip3-+` `sum-log` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-+l-` `sub-neg` `pow1/3` `diff-log` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

12.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
12.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
20.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
18.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
165.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
52.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
60.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	333	1608
1	1288	1250
2	5001	1106

prune593.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 3 expressions with local error:

2.5b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.1b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
8.5b	(* (pow z 2) y)

rewrite10.0ms

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)))
2.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
6.0ms	(* (pow z 2) y)

series179.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
97.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
22.0ms	(* (pow z 2) y)

simplify149.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (141.0ms)

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

prune254.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.8b

regimes441.0ms

Accuracy

73.6% (4.4b remaining)

Error of 9.1b against oracle of 4.7b and baseline of 21.5b

bsearch120.0ms

Steps

Iters	Range		Point
5	4.2185849944799077e-221	9.771091612138487e-221	9.274120679861768e-221
7	-91.73841076085421	-0.49115008736797033	-0.4984438493979181

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	32
1	46	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

761.0ms	1451×	body	1280	valid
726.0ms	1483×	body	10240	exit
450.0ms	1536×	body	640	valid
214.0ms	3588×	body	80	valid
163.0ms	886×	body	320	valid
85.0ms	2409×	body	80	nan
85.0ms	66×	body	2560	valid
55.0ms	500×	body	160	valid
53.0ms	259×	body	640	nan
33.0ms	112×	body	1280	nan
25.0ms	196×	body	320	nan
9.0ms	113×	body	160	nan