Details

sample96.0ms

Algorithm

intervals

Results

28.0ms	49×	body	1280	valid
16.0ms	61×	body	640	valid
12.0ms	25×	body	10240	exit
6.0ms	97×	body	80	valid
4.0ms	24×	body	320	valid
3.0ms	3×	body	2560	valid
2.0ms	23×	body	160	valid
2.0ms	68×	body	80	nan
2.0ms	10×	body	640	nan
1.0ms	6×	body	1280	nan
1.0ms	25×	body	80	overflowed
0.0ms	6×	body	160	nan
0.0ms	2×	body	320	nan

simplify218.0ms

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: 27.6b

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)
2.6b	(log (+ (- 1.0 y) (* y (exp z))))
2.8b	(+ (- 1.0 y) (* y (exp z)))

rewrite56.0ms

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)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
15.0ms	(+ (- 1.0 y) (* y (exp z)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
154.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
74.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune379.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
1.8b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.5b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
8.1b	(* (pow z 2) y)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
50×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
11×	`add-exp-log`
8×	`associate-l` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`fma-neg` `associate-r` `prod-exp` `associate-/r` `associate-/l`
2×	`unpow2` `difference-of-squares` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `pow-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--`

Counts

4 → 127

Calls

4 calls:

7.0ms	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
2.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
6.0ms	(* (pow z 2) y)

series298.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- x (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t))
60.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
95.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
21.0ms	(* (pow z 2) y)

simplify71.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	545	3031
1	1954	1985
2	5001	1748

prune404.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.4b	(/ (* z y) t)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`times-frac` `fma-neg` `associate-/r*`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `diff-log` `div-exp` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 53

Calls

2 calls:

39.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
3.0ms	(/ (* z y) t)

series106.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
19.0ms	(/ (* z y) t)

simplify39.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	261	704
1	1021	433
2	5001	422

prune182.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ 1 (/ t (* z y)))) (/ (log 1.0) t)))
0.6b	(/ 1 (/ t (* z y)))
4.1b	(/ t (* z y))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
30×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-exp-log`
28×	`add-cube-cbrt`
17×	`add-cbrt-cube`
14×	`div-exp`
9×	`prod-diff`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
4×	`pow1` `prod-exp`
3×	`expm1-log1p-u` `rec-exp` `fma-neg` `1-exp` `log1p-expm1-u`
2×	`frac-2neg` `diff-log` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-flip` `sum-log` `associate-/r/` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

3 → 111

Calls

3 calls:

61.0ms	(- x (+ (* 1.0 (/ 1 (/ t (* z y)))) (/ (log 1.0) t)))
6.0ms	(/ 1 (/ t (* z y)))
3.0ms	(/ t (* z y))

series165.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(- x (+ (* 1.0 (/ 1 (/ t (* z y)))) (/ (log 1.0) t)))
22.0ms	(/ 1 (/ t (* z y)))
23.0ms	(/ t (* z y))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	433	1108
1	1807	748
2	5002	693

prune247.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

regimes598.0ms

Accuracy

63.7% (4.8b remaining)

Error of 8.8b against oracle of 3.9b and baseline of 17.2b

bsearch62.0ms

Steps

Iters	Range		Point
6	-5.629504045830355e-12	-1.3960179899419418e-12	-3.6327701783805246e-12

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

757.0ms	1439×	body	1280	valid
461.0ms	1566×	body	640	valid
395.0ms	802×	body	10240	exit
219.0ms	3586×	body	80	valid
168.0ms	912×	body	320	valid
93.0ms	2531×	body	80	nan
90.0ms	70×	body	2560	valid
51.0ms	459×	body	160	valid
47.0ms	239×	body	640	nan
35.0ms	122×	body	1280	nan
34.0ms	762×	body	80	overflowed
26.0ms	193×	body	320	nan
10.0ms	120×	body	160	nan