Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	399×	body	80	nan
19.0ms	378×	body	80	valid

simplify55.0ms

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: 7.5b

localize16.0ms

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))
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite75.0ms

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:

28.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
9.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

441.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
437.0ms	(- (* (- x 0.5) (log x)) x)
257.0ms	(* (- x 0.5) (log x))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (37.0ms)

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

prune411.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt x)) (- x 0.5))
0.2b	(* (- x 0.5) (log (sqrt x)))
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite122.0ms

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))
13.0ms	(* (- x 0.5) (log (sqrt x)))
70.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series486.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (log (sqrt x)) (- x 0.5))
106.0ms	(* (- x 0.5) (log (sqrt x)))
190.0ms	(+ (* (- 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)

simplify77.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (63.0ms)

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

prune896.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite25.0ms

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

series616.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
176.0ms	(cbrt x)
173.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify97.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (91.0ms)

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

prune381.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
6.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-prod`
9×	`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 → 63

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (* (cbrt x) (cbrt x)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series794.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
247.0ms	(cbrt (cbrt x))
282.0ms	(cbrt (* (cbrt x) (cbrt x)))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify118.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	277	521
1	865	471
2	4142	458
3	5002	454

prune430.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes298.0ms

Accuracy

76.2% (0.3b remaining)

Error of 5.3b against oracle of 5.0b and baseline of 6.2b

bsearch52.0ms

Steps

Iters	Range		Point
5	7.540004042657862e+120	1.5765673566733113e+121	1.5593569426205532e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	33
1	58	33

end0.0ms

sample1.7s

Algorithm

intervals

Results

608.0ms	11814×	body	80	valid
547.0ms	12023×	body	80	nan