Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	366×	body	80	valid
17.0ms	390×	body	80	nan

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
5.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
7×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

21.0ms	(* (+ y 0.0007936500793651) z)
44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
52.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series290.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (+ y 0.0007936500793651) z)
40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
130.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	446	778
1	1546	696
2	5002	694

prune361.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (log x) (- x 0.5))
5.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
101×	`prod-diff`
88×	`add-cube-cbrt`
68×	`associate-+r+`
54×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`add-log-exp`
10×	`add-exp-log` `flip3--` `associate-*r/` `add-cbrt-cube` `flip--`
9×	`pow1`
8×	`associate-r` `frac-add`
7×	`associate-l`
6×	`div-inv`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `associate-/l`
2×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `frac-2neg` `div-exp` `clear-num` `log-pow` `associate--r-`

Counts

4 → 215

Calls

4 calls:

250.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
25.0ms	(* (log x) (- x 0.5))
53.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series529.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
255.0ms	(* (log x) (- x 0.5))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify141.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1253	3523
1	4882	3081
2	5001	3081

prune776.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
0.3b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
5.0b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite134.0ms

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`
6×	`div-inv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
51.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
33.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series395.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
130.0ms	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
97.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
123.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify77.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	682	1925
1	2964	1734
2	5001	1648

prune480.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
5.2b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`-un-lft-identity` `associate-r*`
17×	`add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1` `associate-l`
6×	`associate-*l/` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`frac-times` `div-exp`
1×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `flip--` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

20.0ms	(* (+ y 0.0007936500793651) z)
43.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
88.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ y 0.0007936500793651) z)
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
131.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
88.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify65.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	555	864
1	2213	758
2	5001	738

prune364.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 1.6b

regimes437.0ms

Accuracy

82% (0.7b remaining)

Error of 2.6b against oracle of 1.9b and baseline of 6.0b

bsearch93.0ms

Steps

Iters	Range		Point
6	1.8312902555256415e+216	1.15903585461275e+217	4.717658198318119e+216
4	8.654798412012067e+100	1.336688849854629e+101	8.80205122721626e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	35
1	61	35

end0.0ms

sample2.0s

Algorithm

intervals

Results

725.0ms	11633×	body	80	nan
604.0ms	11662×	body	80	valid