Details

sample61.0ms

Algorithm

intervals

Results

19.0ms	370×	body	80	nan
19.0ms	372×	body	80	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

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

prune10.0ms

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

6.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
19.0ms	(* (- (* (+ 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)))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series274.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
121.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	432	812
1	1472	709
2	5003	707

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

30.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

427.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
420.0ms	(- (* (- x 0.5) (log x)) x)
250.0ms	(* (- x 0.5) (log x))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	576	925
1	2275	825
2	5001	802

prune464.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series622.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
175.0ms	(cbrt x)
178.0ms	(cbrt x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify106.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	223	484
1	699	441
2	3468	432
3	5001	425

prune421.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
65×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
19×	`add-exp-log`
16×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`log-prod`
8×	`pow1` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `div-inv` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`prod-diff`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `associate-/r/` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

8.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
5.0ms	(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
2.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

series879.0ms

Counts

4 → 12

Calls

4 calls:

424.0ms	(- (* (- x 0.5) (log x)) x)
259.0ms	(* (- x 0.5) (log x))
81.0ms	(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
114.0ms	(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

simplify109.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	692	1623
1	3301	1454
2	5002	1380

prune494.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.4b

regimes350.0ms

Accuracy

86.3% (0.5b remaining)

Error of 2.7b against oracle of 2.2b and baseline of 6.1b

bsearch181.0ms

Steps

Iters	Range		Point
9	1.4488975596305785e+198	6.189408123833058e+205	1.2009024989148773e+200
9	91983697529749.86	3.208423007490159e+19	3317354487842124.5

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	42
1	67	42

end0.0ms

sample1.7s

Algorithm

intervals

Results

619.0ms	11786×	body	80	valid
525.0ms	11664×	body	80	nan