Details

sample80.0ms

Algorithm

intervals

Results

23.0ms	46×	body	1280	valid
11.0ms	43×	body	640	valid
8.0ms	133×	body	80	valid
4.0ms	84×	body	80	overflowed
4.0ms	3×	body	2560	valid
3.0ms	17×	body	320	valid
2.0ms	66×	body	80	nan
2.0ms	14×	body	160	valid
2.0ms	9×	body	640	nan
1.0ms	3×	body	1280	nan
1.0ms	7×	body	160	nan
0.0ms	4×	body	320	nan

simplify266.0ms

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: 21.4b

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)
1.8b	(+ (- 1.0 y) (* y (exp z)))
1.9b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite118.0ms

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:

11.0ms	(* y (exp z))
52.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
31.0ms	(+ (- 1.0 y) (* y (exp z)))
21.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
156.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
33.0ms	(+ (- 1.0 y) (* y (exp z)))
71.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

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

prune544.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite26.0ms

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:

6.0ms	(* y (expm1 z))
14.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series240.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* y (expm1 z))
139.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
67.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (42.0ms)

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

prune250.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.0b	(* y (expm1 z))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite33.0ms

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:

5.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(* y (expm1 z))
12.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
38.0ms	(* y (expm1 z))
71.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
70.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify90.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (74.0ms)

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

prune417.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
0.1b	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
3.3b	(log (+ 1.0 (* y (expm1 z))))
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
46×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
37×	`sqrt-prod`
25×	`associate-r`
16×	`pow1`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`log-pow`
7×	`associate-l` `associate-/l*`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `rem-log-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
24.0ms	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
4.0ms	(log (+ 1.0 (* y (expm1 z))))
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series1.0s

Counts

4 → 12

Calls

4 calls:

746.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
148.0ms	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
74.0ms	(log (+ 1.0 (* y (expm1 z))))
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify75.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	636	1804
1	2627	1583
2	5001	1512

prune485.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.6b

regimes269.0ms

Accuracy

42.1% (4.4b remaining)

Error of 5.6b against oracle of 1.2b and baseline of 8.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

sample2.5s

Algorithm

intervals

Results

696.0ms	1388×	body	1280	valid
385.0ms	1437×	body	640	valid
223.0ms	3962×	body	80	valid
125.0ms	742×	body	320	valid
116.0ms	2510×	body	80	overflowed
99.0ms	79×	body	2560	valid
99.0ms	2723×	body	80	nan
54.0ms	289×	body	640	nan
45.0ms	420×	body	160	valid
36.0ms	130×	body	1280	nan
25.0ms	206×	body	320	nan
9.0ms	119×	body	160	nan