Details

sample105.0ms

Algorithm

intervals

Results

24.0ms	44×	body	1280	valid
22.0ms	46×	body	10240	exit
17.0ms	61×	body	640	valid
6.0ms	36×	body	320	valid
6.0ms	94×	body	80	valid
4.0ms	3×	body	2560	valid
3.0ms	102×	body	80	nan
2.0ms	19×	body	160	valid
1.0ms	6×	body	640	nan
1.0ms	7×	body	320	nan
0.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan

simplify212.0ms

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: 25.5b

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)
2.5b	(+ (- 1.0 y) (* y (exp z)))
2.6b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite62.0ms

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))
24.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
20.0ms	(+ (- 1.0 y) (* y (exp z)))
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* y (exp z))
168.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
36.0ms	(+ (- 1.0 y) (* y (exp z)))
77.0ms	(log (+ (- 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

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
5.4b	(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))))

series276.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* y (expm1 z))
162.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify58.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (44.0ms)

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

prune244.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
0.2b	(pow (log (fma (expm1 z) y 1.0)) 3)
0.2b	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
5.4b	(log (fma (expm1 z) y 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
18×	`pow1`
17×	`associate-/l*`
13×	`log-pow`
8×	`add-exp-log`
6×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 151

Calls

4 calls:

8.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
2.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
2.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
1.0ms	(log (fma (expm1 z) y 1.0))

series416.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
157.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
68.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
63.0ms	(log (fma (expm1 z) y 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	743	1625
1	3366	1502
2	5001	1489

prune419.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0))))
5.4b	(log (fma (expm1 z) y 1.0))
5.4b	(log (fma (expm1 z) y 1.0))
5.4b	(log (fma (expm1 z) y 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `log-pow`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 53

Calls

4 calls:

2.0ms	(cbrt (* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series480.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0))))
67.0ms	(log (fma (expm1 z) y 1.0))
61.0ms	(log (fma (expm1 z) y 1.0))
67.0ms	(log (fma (expm1 z) y 1.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	524	816
1	2291	741
2	5001	735

prune296.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

regimes228.0ms

Accuracy

40.7% (3.9b remaining)

Error of 8.6b against oracle of 4.7b and baseline of 11.3b

bsearch84.0ms

Steps

Iters	Range		Point
8	-7.623449813706084e-69	-8.989668196499857e-73	-2.1255354070387358e-69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample3.1s

Algorithm

intervals

Results

757.0ms	1442×	body	1280	valid
751.0ms	1516×	body	10240	exit
450.0ms	1570×	body	640	valid
208.0ms	3529×	body	80	valid
169.0ms	938×	body	320	valid
120.0ms	97×	body	2560	valid
97.0ms	2548×	body	80	nan
52.0ms	266×	body	640	nan
50.0ms	451×	body	160	valid
30.0ms	106×	body	1280	nan
20.0ms	154×	body	320	nan
7.0ms	87×	body	160	nan