Details

sample102.0ms

Algorithm

intervals

Results

43.0ms	362×	body	80	valid
34.0ms	367×	body	80	nan

simplify65.0ms

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: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite72.0ms

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:

29.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

460.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
459.0ms	(- (* (- x 0.5) (log x)) x)
275.0ms	(* (- x 0.5) (log x))
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (46.0ms)

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

prune450.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
0.2b	(* (log (sqrt x)) (- x 0.5))
0.2b	(* (log (sqrt x)) (- x 0.5))
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

6.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
16.0ms	(* (log (sqrt x)) (- x 0.5))
11.0ms	(* (log (sqrt x)) (- x 0.5))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series498.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
108.0ms	(* (log (sqrt x)) (- x 0.5))
121.0ms	(* (log (sqrt x)) (- x 0.5))
95.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	398	894
1	1397	837
2	5001	828

prune502.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite24.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series914.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt x)
195.0ms	(cbrt x)
425.0ms	(cbrt x)
97.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify119.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (112.0ms)

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

prune428.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
5.2b	(pow (/ 1 x) -1/3)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
4.0ms	(pow (/ 1 x) -1/3)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series683.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt x)
204.0ms	(cbrt x)
191.0ms	(pow (/ 1 x) -1/3)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	365	578
1	1288	520
2	5001	507

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

regimes388.0ms

Accuracy

74.8% (0.3b remaining)

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

bsearch125.0ms

Steps

Iters	Range		Point
9	2.0223808950029185e+133	2.33008206468221e+138	9.622718526139006e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	41
1	60	41

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	11642×	body	80	valid
1.1s	11635×	body	80	nan