Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	376×	body	80	valid
17.0ms	368×	body	80	nan

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.7b

Counts

2 → 2

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
38×	`associate-l`
30×	`add-sqr-sqrt`
26×	`distribute-lft-out`
24×	`times-frac`
21×	`add-cube-cbrt`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/l*`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

4 → 111

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
14.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
26.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series286.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ y 0.0007936500793651) z)
40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
128.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	451	963
1	1553	881
2	5002	879

prune294.0ms

Filtered

123 candidates to 81 candidates (65.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 3.0b

Counts

125 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

563×	`*-un-lft-identity`
221×	`add-sqr-sqrt`
185×	`prod-diff`
162×	`associate-l`
150×	`add-cube-cbrt`
148×	`distribute-lft-out`
144×	`times-frac`
143×	`associate-+r+`
111×	`distribute-lft-out--`
70×	`flip3--` `associate-*r/` `flip--`
68×	`frac-add`
64×	`frac-sub`
40×	`associate-/l*`
32×	`difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
15×	`fma-def` `associate-/r*`
13×	`pow1` `associate-r` `add-log-exp`
12×	`associate-+r-`
11×	`associate--r+`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
6×	`sub-neg` `flip3-+` `flip-+` `div-inv`
5×	`frac-2neg` `clear-num` `log-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log` `sum-log` `*-commutative`
2×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `div-exp` `associate--r-`

Counts

4 → 409

Calls

4 calls:

14.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
71.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
7.0ms	(* (log x) (- x 0.5))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series527.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
142.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
255.0ms	(* (log x) (- x 0.5))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify132.0ms

Algorithm

egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2249	8247
1	5003	7511

prune1.2s

Filtered

421 candidates to 216 candidates (51.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	415	6	421
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	417	12	429

Merged error: 3.0b

Counts

429 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(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)))
5.2b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
210×	`times-frac`
112×	`associate-l`
107×	`add-sqr-sqrt`
103×	`distribute-lft-out`
100×	`add-cube-cbrt`
54×	`distribute-lft-out--`
46×	`associate-/r*`
24×	`associate-/r/`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`div-inv`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r`
2×	`rec-exp` `1-exp` `associate-*l/` `remove-double-div` `difference-of-squares` `unswap-sqr`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `inv-pow`

Counts

4 → 249

Calls

4 calls:

14.0ms	(* (- (* (+ 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)))
30.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
22.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series408.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
137.0ms	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
100.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
129.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify110.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	694	2617
1	2992	2364
2	5001	2208

prune439.0ms

Filtered

261 candidates to 112 candidates (42.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	260	13	273

Merged error: 2.1b

Counts

273 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.4b	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
0.4b	(* (log x) (+ (sqrt x) (sqrt 0.5)))
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

849×	`*-un-lft-identity`
338×	`add-sqr-sqrt`
293×	`prod-diff`
282×	`associate-*r/`
272×	`frac-add`
267×	`associate-l`
256×	`frac-sub`
250×	`add-cube-cbrt`
241×	`flip3--` `flip--`
228×	`distribute-lft-out`
162×	`sqrt-prod`
149×	`distribute-lft-out--`
144×	`times-frac`
143×	`associate-+r+`
140×	`frac-times`
136×	`associate-/l*`
124×	`flip3-+` `flip-+`
78×	`distribute-rgt-in` `distribute-lft-in`
76×	`associate-+l+`
70×	`associate-*l/`
51×	`associate-/r*`
36×	`difference-of-squares`
34×	`associate-/l/`
33×	`associate-r`
31×	`fma-def`
17×	`pow1` `frac-2neg` `clear-num`
13×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
12×	`associate-+r-`
11×	`associate--r+`
9×	`unswap-sqr`
6×	`sub-neg` `log-pow` `div-inv`
5×	`*-commutative`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`+-commutative` `diff-log` `sum-log`
1×	`cbrt-undiv` `div-exp` `associate--r-`

Counts

4 → 767

Calls

4 calls:

99.0ms	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
22.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
8.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series751.0ms

Counts

4 → 12

Calls

4 calls:

387.0ms	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
197.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
74.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
92.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify344.0ms

Algorithm

egg-herbie

Counts

779 → 779

Iterations

Useful iterations: 1 (105.0ms)

Iter	Nodes	Cost
0	4823	28661
1	5001	28494

prune2.8s

Filtered

779 candidates to 429 candidates (55.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	775	4	779
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	779	13	792

Merged error: 2.1b

Counts

792 → 13

regimes521.0ms

Accuracy

73.8% (1.1b remaining)

Error of 3.2b against oracle of 2.2b and baseline of 6.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	43
1	59	43

end0.0ms

sample1.6s

Algorithm

intervals

Results

617.0ms	11614×	body	80	valid
526.0ms	11479×	body	80	nan