Details

sample70.0ms

Algorithm

intervals

Results

25.0ms	390×	body	80	valid
21.0ms	425×	body	80	nan

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 7.7b

localize19.0ms

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))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite40.0ms

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:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
9.0ms	(* (- 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:

425.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
412.0ms	(- (* (- x 0.5) (log x)) x)
251.0ms	(* (- x 0.5) (log x))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

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

prune401.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

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

series630.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
185.0ms	(cbrt x)
179.0ms	(cbrt x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify101.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	212	462
1	697	420
2	3321	413
3	5001	410

prune377.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
5.1b	(pow x 1/3)
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(pow x 1/3)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series620.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
183.0ms	(cbrt x)
174.0ms	(pow x 1/3)
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify35.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	268	467
1	1047	415
2	5001	409

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x)
0.4b	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
0.4b	(* (- (sqrt x) (sqrt 0.5)) (log x))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

16.0ms	(- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x)
18.0ms	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
9.0ms	(* (- (sqrt x) (sqrt 0.5)) (log x))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series792.0ms

Counts

4 → 12

Calls

4 calls:

426.0ms	(- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x)
197.0ms	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
82.0ms	(* (- (sqrt x) (sqrt 0.5)) (log x))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify107.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1014	1764
1	4324	1337
2	5001	1320

prune546.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

regimes357.0ms

Accuracy

76.9% (0.3b remaining)

Error of 5.2b against oracle of 4.9b and baseline of 6.1b

bsearch80.0ms

Steps

Iters	Range		Point
7	4.9375425573450695e+130	9.425189884413038e+132	2.056781149069935e+132

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	43
1	66	43

end0.0ms

sample1.7s

Algorithm

intervals

Results

669.0ms	11727×	body	80	valid
573.0ms	11555×	body	80	nan