Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	420×	body	80	nan
21.0ms	387×	body	80	valid

simplify56.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

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)))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite54.0ms

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:

9.0ms	(* (+ y 0.0007936500793651) z)
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series268.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ y 0.0007936500793651) z)
42.0ms	(* (- (* (+ 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)))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

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

prune358.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

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))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite200.0ms

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:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
131.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
15.0ms	(* (log x) (- x 0.5))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series531.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
134.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
274.0ms	(* (log x) (- x 0.5))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify138.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (27.0ms)

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

prune829.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
4.3b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
101×	`prod-diff`
86×	`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×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube`
7×	`pow1`
6×	`div-inv`
5×	`sub-neg` `associate-r`
4×	`expm1-log1p-u` `associate-l` `frac-sub` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
54.0ms	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series506.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
140.0ms	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
253.0ms	(* (log x) (- x 0.5))
77.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify128.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1130	3190
1	4346	2778
2	5001	2778

prune818.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(+ (* (log x) (- x 0.5)) (- (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
4.5b	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
41×	`prod-diff`
39×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
19×	`associate-*r/`
18×	`associate-r`
15×	`add-exp-log`
13×	`flip3--` `flip--` `add-log-exp`
12×	`frac-add`
11×	`times-frac` `add-cbrt-cube`
9×	`pow1`
8×	`associate-+r+` `frac-sub`
7×	`associate-l`
5×	`sub-neg` `prod-exp` `un-div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log` `sum-log` `cbrt-unprod`
2×	`div-exp` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `rec-exp` `fma-def` `flip3-+` `1-exp` `log-pow` `flip-+` `fma-udef` `div-inv` `associate--r-`

Counts

4 → 154

Calls

4 calls:

1.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
49.0ms	(+ (* (log x) (- x 0.5)) (- (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
8.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

series526.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
140.0ms	(+ (* (log x) (- x 0.5)) (- (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
255.0ms	(* (log x) (- x 0.5))
95.0ms	(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

simplify131.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1017	2083
1	4458	1737
2	5001	1737

prune560.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

regimes329.0ms

Accuracy

69.8% (0.4b remaining)

Error of 5.2b against oracle of 4.7b and baseline of 6.2b

bsearch49.0ms

Steps

Iters	Range		Point
5	1.0022106025890555e+122	2.6317850520112385e+122	2.4536597575730546e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	44	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

662.0ms	11788×	body	80	valid
564.0ms	11982×	body	80	nan