Details

sample59.0ms

Algorithm

intervals

Results

19.0ms	358×	body	80	valid
17.0ms	372×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
0.1b	(fma (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)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
75×	`add-cube-cbrt`
74×	`prod-diff`
64×	`times-frac`
16×	`distribute-lft-out--`
15×	`difference-of-squares`
13×	`fma-neg`
11×	`associate--r+`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`sub-neg` `associate-*l/` `frac-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

77.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series334.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
122.0ms	(fma (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)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify85.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	737	3116
1	2431	2540
2	5002	2408

prune570.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

11.0ms	(* (- x 0.5) (log x))
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
32.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series832.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (- x 0.5) (log x))
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
449.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	606	918
1	2446	804
2	5001	788

prune464.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite23.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series762.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt x)
323.0ms	(cbrt x)
180.0ms	(cbrt x)
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (96.0ms)

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

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
4.9b	(pow x 1/3)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
35.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
1.0ms	(pow x 1/3)

series639.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
183.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
196.0ms	(pow x 1/3)

simplify36.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	281	489
1	1061	429
2	5001	423

prune479.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

regimes422.0ms

Accuracy

67.1% (0.9b remaining)

Error of 4.0b against oracle of 3.1b and baseline of 5.9b

bsearch94.0ms

Steps

Iters	Range		Point
8	400742927599967.94	3.4507373641305165e+17	3.911764701695799e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	33
1	55	33
2	55	33

end0.0ms

sample1.7s

Algorithm

intervals

Results

639.0ms	11593×	body	80	valid
566.0ms	11742×	body	80	nan