Details

sample99.0ms

Algorithm

intervals

Results

41.0ms	392×	body	80	valid
33.0ms	401×	body	80	nan

simplify64.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.1b

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)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite56.0ms

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:

10.0ms	(* (+ y 0.0007936500793651) z)
20.0ms	(* (- (* (+ 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)))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series284.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ y 0.0007936500793651) z)
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
126.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

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

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize18.0ms

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))
5.7b	(/ (+ (* (- (* (+ 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:

20.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
136.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series539.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
135.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
273.0ms	(* (log x) (- x 0.5))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify147.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (30.0ms)

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

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

localize22.0ms

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)))
0.4b	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

209×	`prod-diff`
195×	`add-sqr-sqrt`
193×	`*-un-lft-identity`
159×	`add-cube-cbrt`
152×	`sqrt-prod`
77×	`distribute-rgt-in` `distribute-lft-in`
76×	`associate-+l+`
68×	`associate-+r+`
54×	`times-frac`
42×	`associate-*r/`
32×	`frac-add`
31×	`flip3--` `flip--`
20×	`frac-times`
18×	`flip3-+` `flip-+`
17×	`difference-of-squares`
16×	`frac-sub`
15×	`distribute-lft-out--`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
12×	`pow1`
10×	`associate-*l/`
6×	`div-inv`
5×	`sub-neg` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `associate-/l`
2×	`*-commutative` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `frac-2neg` `div-exp` `clear-num` `log-pow` `associate--r-` `unswap-sqr`

Counts

4 → 361

Calls

4 calls:

170.0ms	(+ (* (* (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)))
49.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series730.0ms

Counts

4 → 12

Calls

4 calls:

386.0ms	(+ (* (* (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)))
71.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
188.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2369	9697
1	5003	8331

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (* (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)))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (* (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)))
21.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
26.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series561.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
360.0ms	(fma (* (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)))
76.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify78.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	606	1018
1	2414	884
2	5002	869

prune415.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

regimes439.0ms

Accuracy

85.8% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 6.0b

bsearch80.0ms

Steps

Iters	Range		Point
7	103975187.10285737	8547641608.38307	8439582884.126038

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	22
1	42	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	11723×	body	80	valid
1.0s	11935×	body	80	nan