Details

sample102.0ms

Algorithm

intervals

Results

23.0ms	45×	body	1280	valid
22.0ms	44×	body	10240	exit
16.0ms	55×	body	640	valid
7.0ms	116×	body	80	valid
5.0ms	4×	body	2560	valid
3.0ms	20×	body	320	valid
3.0ms	82×	body	80	nan
2.0ms	16×	body	160	valid
2.0ms	5×	body	1280	nan
1.0ms	7×	body	640	nan
0.0ms	3×	body	320	nan
0.0ms	1×	body	160	nan

simplify220.0ms

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: 25.1b

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))))
2.6b	(+ (- 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)
12.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
160.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
79.0ms	(log (+ (- 1.0 y) (* y (exp z))))
37.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

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

prune367.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.9b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
20×	`pow1`
14×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `flip3-+` `fma-neg` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate--r-` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

10.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
38.0ms	(* y (expm1 z))
164.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify89.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	746	2869
1	2769	1983
2	5001	1785

prune387.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`add-exp-log` `associate-r`
11×	`times-frac` `add-cbrt-cube`
10×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-neg` `prod-diff` `cbrt-unprod`
2×	`log-div` `div-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `flip3-+` `diff-log` `1-exp` `associate-*r/` `rem-log-exp` `un-div-inv` `flip--` `flip-+` `div-inv`

Counts

4 → 95

Calls

4 calls:

2.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
3.0ms	(* y (expm1 z))
9.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- x (* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t)))
43.0ms	(* y (expm1 z))
158.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
80.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify73.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	598	881
1	2528	770
2	5001	730

prune359.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.8b

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))))

rewrite20.0ms

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))
3.0ms	(/ 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))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* y (expm1 z))
213.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
81.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
79.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify89.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (71.0ms)

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

prune388.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 4.8b

regimes412.0ms

Accuracy

35.9% (4.6b remaining)

Error of 9.3b against oracle of 4.8b and baseline of 11.9b

bsearch117.0ms

Steps

Iters	Range		Point
6	6.346608773331219e-226	3.599959993217496e-225	3.4446276387824773e-225
6	-3.617724343655394e-05	-3.563044520560046e-06	-3.6124775496653163e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

760.0ms	1427×	body	1280	valid
743.0ms	1474×	body	10240	exit
463.0ms	1574×	body	640	valid
211.0ms	3533×	body	80	valid
165.0ms	907×	body	320	valid
108.0ms	80×	body	2560	valid
88.0ms	2494×	body	80	nan
56.0ms	510×	body	160	valid
53.0ms	261×	body	640	nan
35.0ms	119×	body	1280	nan
26.0ms	197×	body	320	nan
8.0ms	98×	body	160	nan