Details

sample111.0ms

Algorithm

intervals

Results

30.0ms	60×	body	10240	exit
16.0ms	33×	body	1280	valid
16.0ms	55×	body	640	valid
10.0ms	5×	body	2560	valid
7.0ms	117×	body	80	valid
6.0ms	34×	body	320	valid
2.0ms	62×	body	80	nan
2.0ms	11×	body	640	nan
2.0ms	15×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	7×	body	320	nan
0.0ms	2×	body	160	nan

simplify203.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	710	7
9	1092	7
10	1240	7
11	1558	7
12	4191	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.4b	(log (+ (- 1.0 y) (* y (exp z))))
4.1b	(+ (- 1.0 y) (* y (exp z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `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` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))
6.0ms	(+ (- 1.0 y) (* y (exp z)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
154.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
85.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5001	726

prune289.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.3b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-r`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

5.0ms	(* 0.5 (pow z 2))
5.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
6.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series296.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow z 2))
66.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
85.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
121.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	415	800
1	1832	721
2	5001	715

prune342.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.4b	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.4b	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
60×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

4.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
7.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
9.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
4.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
161.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
87.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
240.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	649	2208
1	3269	2018
2	5001	1932

prune455.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
20.8b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
20.8b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
20.8b	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
3.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
3.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

89.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
327.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
316.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))
319.0ms	(cbrt (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	374	1161
1	1546	1097
2	5001	1007

prune357.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 5.1b

regimes660.0ms

Accuracy

74.3% (4.2b remaining)

Error of 8.7b against oracle of 4.5b and baseline of 20.7b

bsearch136.0ms

Steps

Iters	Range		Point
8	2.5548096550536154e-78	5.333502830476792e-74	2.802488273816828e-74
6	-5.8829093822384e-14	-7.856438118040365e-15	-5.458414998494592e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	25
1	53	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

760.0ms	1518×	body	10240	exit
732.0ms	1352×	body	1280	valid
459.0ms	1531×	body	640	valid
224.0ms	3637×	body	80	valid
170.0ms	911×	body	320	valid
128.0ms	97×	body	2560	valid
93.0ms	2422×	body	80	nan
59.0ms	505×	body	160	valid
53.0ms	265×	body	640	nan
32.0ms	99×	body	1280	nan
26.0ms	190×	body	320	nan
9.0ms	106×	body	160	nan