Details

sample71.0ms

Algorithm

intervals

Results

26.0ms	386×	body	80	valid
22.0ms	327×	body	80	nan

simplify63.0ms

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

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: 6.7b

Counts

2 → 2

localize15.0ms

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)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite50.0ms

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:

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

series315.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
118.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify94.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (64.0ms)

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

prune459.0ms

Filtered

186 candidates to 111 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	8	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Merged error: 4.1b

Counts

188 → 9

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))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite40.0ms

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:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

422.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
415.0ms	(- (* (- x 0.5) (log x)) x)
249.0ms	(* (- x 0.5) (log x))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (59.0ms)

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

prune402.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	124	13	137

Merged error: 4.1b

Counts

137 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

15.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

768.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
182.0ms	(cbrt x)
173.0ms	(cbrt x)
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	680	1100
1	2677	947
2	5001	914

prune579.0ms

Filtered

124 candidates to 113 candidates (91.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	3	8	11
Picked	1	0	1
Done	1	0	1
Total	127	10	137

Merged error: 4.1b

Counts

137 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (- x 0.5) (* 2 (log (cbrt x))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

1.0ms	(fma (- x 0.5) (* 2 (log (cbrt x))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

941.0ms	(fma (- x 0.5) (* 2 (log (cbrt x))) (* (- x 0.5) (log (cbrt x))))
178.0ms	(cbrt x)
182.0ms	(cbrt x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify145.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	293	598
1	916	530
2	4534	509
3	5001	509

prune328.0ms

Filtered

79 candidates to 71 candidates (89.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 4.1b

Counts

89 → 10

regimes378.0ms

Accuracy

64.8% (1.0b remaining)

Error of 4.1b against oracle of 3.1b and baseline of 6.0b

bsearch84.0ms

Steps

Iters	Range		Point
8	14.716166499582775	568598.8407081462	552987.9654093346

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

784.0ms	11634×	body	80	valid
702.0ms	11469×	body	80	nan