Details

sample74.0ms

Algorithm

intervals

Results

25.0ms	381×	body	80	nan
25.0ms	372×	body	80	valid

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: 5.9b

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)))
5.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
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)

series281.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ y 0.0007936500793651) z)
38.0ms	(* (- (* (+ 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)))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	446	778
1	1546	696
2	5002	694

prune328.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	7	100

Merged error: 4.5b

Counts

100 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
0.1b	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
5.4b	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

4.0ms	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
6.0ms	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
10.0ms	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

series275.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
39.0ms	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
124.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
85.0ms	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	440	952
1	1582	803
2	5003	794

prune311.0ms

Filtered

106 candidates to 77 candidates (72.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 4.5b

Counts

113 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite41.0ms

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:

11.0ms	(+ (- (* (- 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)

series1.4s

Counts

4 → 12

Calls

4 calls:

441.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
639.0ms	(- (* (- x 0.5) (log x)) x)
262.0ms	(* (- x 0.5) (log x))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (60.0ms)

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

prune412.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Merged error: 4.4b

Counts

135 → 9

localize17.0ms

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) (/ 1 x)) (- x 0.91893853320467)))
5.6b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`-un-lft-identity` `associate-r*`
17×	`add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1` `associate-l`
6×	`associate-*l/` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`frac-times` `div-exp`
1×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `flip--` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
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) (/ 1 x)) (- x 0.91893853320467)))
15.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ y 0.0007936500793651) z)
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
124.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
85.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify68.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	555	864
1	2213	758
2	5001	738

prune325.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	109	9	118

Merged error: 4.4b

Counts

118 → 9

regimes361.0ms

Accuracy

83.5% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 5.8b

bsearch92.0ms

Steps

Iters	Range		Point
9	3.5905389242932547e+78	4.809207800058364e+85	4.244600545955558e+78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample2.0s

Algorithm

intervals

Results

792.0ms	11623×	body	80	valid
714.0ms	11793×	body	80	nan