Details

sample105.0ms

Algorithm

intervals

Results

33.0ms	49×	body	1280	valid
18.0ms	47×	body	640	valid
10.0ms	113×	body	80	valid
9.0ms	36×	body	320	valid
4.0ms	72×	body	80	nan
4.0ms	59×	body	80	overflowed
3.0ms	3×	body	2560	valid
3.0ms	9×	body	640	nan
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	2×	body	160	nan

simplify209.0ms

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: 24.0b

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)
0.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.7b	(+ (- 1.0 y) (* y (exp z)))

rewrite59.0ms

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))
23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
19.0ms	(+ (- 1.0 y) (* y (exp z)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* y (exp z))
157.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
79.0ms	(log (+ (- 1.0 y) (* y (exp z))))
40.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (52.0ms)

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

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.9b	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
12.2b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

rewrite34.0ms

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

series497.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt y)
173.0ms	(cbrt y)
92.0ms	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
53.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

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

prune315.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 z)
0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.8b	(log (+ 1.0 (* y (expm1 z))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(expm1 z)
3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(expm1 z)
38.0ms	(* y (expm1 z))
156.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
75.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	441	661
1	1755	607
2	5002	598

prune287.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ 1.0 (* y (expm1 z))))
0.4b	(cbrt (+ 1.0 (* y (expm1 z))))
2.6b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
2.6b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
162.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
143.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
150.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	318	880
1	1062	820
2	5001	794

prune393.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.7b

regimes225.0ms

Accuracy

35% (4.6b remaining)

Error of 9.4b against oracle of 4.8b and baseline of 11.9b

bsearch213.0ms

Steps

Iters	Range		Point
8	1.744684644555791e-189	1.4216327668891872e-185	1.1044357960904684e-185
10	-3.562337332794009e-18	-4.768917922020102e-34	-3.7048441154199694e-33

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample3.2s

Algorithm

intervals

Results

972.0ms	1455×	body	1280	valid
617.0ms	1527×	body	640	valid
313.0ms	3587×	body	80	valid
255.0ms	952×	body	320	valid
155.0ms	2539×	body	80	nan
109.0ms	1534×	body	80	overflowed
107.0ms	76×	body	2560	valid
84.0ms	269×	body	640	nan
72.0ms	435×	body	160	valid
44.0ms	105×	body	1280	nan
41.0ms	195×	body	320	nan
15.0ms	109×	body	160	nan