Details

sample140.0ms

Algorithm

intervals

Results

36.0ms	50×	body	10240	exit
27.0ms	45×	body	1280	valid
21.0ms	54×	body	640	valid
13.0ms	114×	body	80	valid
8.0ms	28×	body	320	valid
6.0ms	95×	body	80	nan
2.0ms	14×	body	160	valid
2.0ms	1×	body	2560	valid
2.0ms	5×	body	1280	nan
1.0ms	4×	body	640	nan
1.0ms	4×	body	320	nan
0.0ms	3×	body	80	overflowed
0.0ms	2×	body	160	nan

simplify242.0ms

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: 25.9b

localize14.0ms

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

rewrite54.0ms

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

series323.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* y (exp z))
173.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
81.0ms	(log (+ (- 1.0 y) (* y (exp z))))
44.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify75.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (60.0ms)

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

prune432.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite14.0ms

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))
7.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series308.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* y (expm1 z))
174.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
85.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify57.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (49.0ms)

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

prune300.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
67×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow1`
20×	`add-exp-log` `associate-/r*`
17×	`log-pow`
13×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

3.0ms	(* y (expm1 z))
2.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* y (expm1 z))
232.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
92.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
86.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify106.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5002	1448

prune700.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

541×	`times-frac`
249×	`add-sqr-sqrt`
247×	`add-cube-cbrt` `*-un-lft-identity`
54×	`pow1`
51×	`add-exp-log`
47×	`log-pow`
34×	`div-exp`
33×	`div-inv`
20×	`associate-/r*` `add-cbrt-cube`
16×	`associate-/l*`
9×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l`
2×	`log-div` `frac-2neg` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 344

Calls

4 calls:

3.0ms	(* y (expm1 z))
2.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
13.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series752.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* y (expm1 z))
526.0ms	(/ 1 (log (+ 1.0 (* y (expm1 z)))))
89.0ms	(/ (/ 1 t) (/ 1 (log (+ 1.0 (* y (expm1 z))))))
87.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify84.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1562	4934
1	5001	4359

prune743.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

regimes414.0ms

Accuracy

36.2% (4.8b remaining)

Error of 9.1b against oracle of 4.3b and baseline of 11.8b

bsearch76.0ms

Steps

Iters	Range		Point
5	-2.4240530748776662e-172	-1.1095929358571949e-172	-2.4006361517684793e-172

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample4.2s

Algorithm

intervals

Results

976.0ms	1463×	body	10240	exit
935.0ms	1452×	body	1280	valid
624.0ms	1581×	body	640	valid
392.0ms	3463×	body	80	valid
255.0ms	946×	body	320	valid
182.0ms	2517×	body	80	nan
135.0ms	93×	body	2560	valid
87.0ms	486×	body	160	valid
80.0ms	278×	body	640	nan
41.0ms	196×	body	320	nan
37.0ms	97×	body	1280	nan
16.0ms	117×	body	160	nan
7.0ms	86×	body	80	overflowed