Details

sample60.0ms

Algorithm

intervals

Results

19.0ms	382×	body	80	valid
17.0ms	390×	body	80	nan

simplify59.0ms

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

prune9.0ms

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

localize19.0ms

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	(* (- (* (+ 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)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite49.0ms

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:

20.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
9.0ms	(* (- (* (+ 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)))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series321.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
120.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify91.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (64.0ms)

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

prune511.0ms

Filtered

186 candidates to 111 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Merged error: 3.2b

Counts

188 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* (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))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite72.0ms

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:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
29.0ms	(+ (* (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))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series492.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
127.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
244.0ms	(* (log x) (- x 0.5))
79.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify145.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (29.0ms)

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

prune785.0ms

Filtered

227 candidates to 155 candidates (68.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	218	9	227
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	222	14	236

Merged error: 3.1b

Counts

236 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (log x) (- x 0.5)) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
0.2b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
5.3b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

450×	`times-frac`
421×	`add-sqr-sqrt`
419×	`*-un-lft-identity`
317×	`add-cube-cbrt`
286×	`prod-diff`
253×	`associate-+r+`
51×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r/`
26×	`div-inv`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`flip3-+` `flip-+`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`pow1` `div-exp` `frac-add`
6×	`associate-/l*`
5×	`sub-neg` `associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-l` `frac-sub` `log1p-expm1-u`
3×	`diff-log` `sum-log`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`+-commutative` `associate-+r-` `pow-flip` `fma-def` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `inv-pow` `associate--r-` `unswap-sqr`

Counts

4 → 464

Calls

4 calls:

63.0ms	(+ (* (log x) (- x 0.5)) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
7.0ms	(* (log x) (- x 0.5))
14.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
11.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series591.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (* (log x) (- x 0.5)) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
257.0ms	(* (log x) (- x 0.5))
89.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
115.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify133.0ms

Algorithm

egg-herbie

Counts

476 → 476

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2246	10128
1	5001	8785

prune1.1s

Filtered

476 candidates to 198 candidates (41.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	475	1	476
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	476	14	490

Merged error: 2.1b

Counts

490 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x) (- x 0.5))
0.2b	(* (log x) (- x 0.5))
0.5b	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
54×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`prod-diff`
28×	`sqrt-pow1`
22×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
18×	`associate-*r/`
14×	`associate-r`
12×	`add-exp-log` `sqrt-div` `associate-l` `add-cbrt-cube`
10×	`pow1/2` `pow-prod-up`
9×	`times-frac`
8×	`flip3--` `flip--`
6×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `swap-sqr` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-*l/` `log-pow` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `rem-square-sqrt` `flip-+` `div-inv`

Counts

4 → 184

Calls

4 calls:

8.0ms	(* (log x) (- x 0.5))
12.0ms	(* (log x) (- x 0.5))
14.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series826.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (log x) (- x 0.5))
252.0ms	(* (log x) (- x 0.5))
232.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify114.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	830	1757
1	3483	1389
2	5003	1358

prune544.0ms

Filtered

196 candidates to 104 candidates (53.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	198	12	210

Merged error: 2.1b

Counts

210 → 12

regimes453.0ms

Accuracy

82.6% (0.7b remaining)

Error of 2.5b against oracle of 1.8b and baseline of 5.9b

bsearch100.0ms

Steps

Iters	Range		Point
7	8.989489765620377e+131	4.887283975934777e+133	4.784196231063594e+133
3	2971428380509416.5	4059825807413484.5	3175502898053929.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	46
1	75	46

end0.0ms

sample1.6s

Algorithm

intervals

Results

607.0ms	11646×	body	80	valid
515.0ms	11744×	body	80	nan