Details

sample71.0ms

Algorithm

intervals

Results

24.0ms	369×	body	80	valid
16.0ms	347×	body	80	nan

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (25.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `prod-diff` `associate-/r` `associate-/l`
2×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

14.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
47.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
57.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series307.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
146.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
96.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	432	812
1	1472	709
2	5003	707

prune374.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

46.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
19.0ms	(- (* (- x 0.5) (log x)) x)
25.0ms	(* (- x 0.5) (log x))
57.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series903.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
482.0ms	(- (* (- x 0.5) (log x)) x)
286.0ms	(* (- x 0.5) (log x))
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	550	878
1	2238	772
2	5001	763

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite64.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
59.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series728.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt x)
207.0ms	(cbrt x)
215.0ms	(cbrt x)
91.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify122.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	223	484
1	699	441
2	3468	432
3	5001	425

prune483.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite10.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series718.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt x)
220.0ms	(cbrt x)
207.0ms	(cbrt x)
86.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	170	423
1	480	383
2	2100	377
3	5001	370

prune680.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

regimes321.0ms

Accuracy

86.1% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 5.7b

bsearch84.0ms

Steps

Iters	Range		Point
7	2.3369654029036e+24	1.3108201729944395e+26	3.0722603425648145e+24

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	32
1	53	32
2	53	32

end0.0ms

sample1.9s

Algorithm

intervals

Results

640.0ms	11661×	body	80	valid
549.0ms	11555×	body	80	nan