Details

sample107.0ms

Algorithm

intervals

Results

45.0ms	386×	body	80	valid
37.0ms	405×	body	80	nan

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

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))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`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` `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 → 98

Calls

4 calls:

26.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

432.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
414.0ms	(- (* (- x 0.5) (log x)) x)
248.0ms	(* (- x 0.5) (log x))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	839
1	1642	776
2	5002	763

prune397.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt` `log-prod`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-log-exp`
12×	`pow1` `associate-+l+` `sqrt-prod`
11×	`associate-r` `associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
6×	`associate-*l/` `log-pow`
5×	`sum-log`
4×	`flip3--` `flip3-+` `frac-add` `flip--` `flip-+`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `associate-+r-` `associate-+r+` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

11.0ms	(* (log (sqrt x)) (- x 0.5))
12.0ms	(* (- x 0.5) (log (sqrt x)))
65.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series465.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (log (sqrt x)) (- x 0.5))
100.0ms	(* (- x 0.5) (log (sqrt x)))
176.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify81.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	715	1457
1	2924	1350
2	5003	1323

prune550.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize22.0ms

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)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite45.0ms

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` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

17.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.0ms	(cbrt x)
1.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

792.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
179.0ms	(cbrt x)
182.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	624	1080
1	2446	943
2	5001	919

prune609.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
0.3b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
4.5b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
66×	`add-cube-cbrt`
24×	`log-prod`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `add-log-exp`
12×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-prod`
11×	`associate-/r/`
9×	`pow1`
8×	`flip3-+` `div-exp` `flip-+`
6×	`associate-r` `associate-l/` `div-inv` `associate-/l`
5×	`associate-l` `sum-log`
4×	`cbrt-undiv` `frac-add`
3×	`flip3--` `log-pow` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`+-commutative` `associate-+l-` `associate-+r-` `associate-+r+` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

12.0ms	(* (- x 0.5) (log (sqrt x)))
65.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
22.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
15.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series510.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (- x 0.5) (log (sqrt x)))
181.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
94.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
122.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify109.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	985	2499
1	4361	2292
2	5001	2200

prune610.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

regimes287.0ms

Accuracy

41.2% (1.2b remaining)

Error of 5.0b against oracle of 3.7b and baseline of 5.8b

bsearch109.0ms

Steps

Iters	Range		Point
8	4.789309294313584e+134	8.932090308940391e+138	9.732204198122952e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	49
1	76	49

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	11711×	body	80	valid
1.1s	11803×	body	80	nan