Details

sample71.0ms

Algorithm

intervals

Results

19.0ms	375×	body	80	valid
18.0ms	417×	body	80	nan

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
3.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
75×	`add-cube-cbrt`
74×	`prod-diff`
64×	`times-frac`
16×	`distribute-lft-out--`
15×	`difference-of-squares`
13×	`fma-neg`
11×	`associate--r+`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`sub-neg` `associate-*l/` `frac-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

149.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
51.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series308.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
35.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
116.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify90.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	737	3116
1	2431	2540
2	5002	2408

prune527.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
3.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

22.0ms	(* (- x 0.5) (log x))
64.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
20.0ms	(- (* (- x 0.5) (log x)) x)
49.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (- x 0.5) (log x))
428.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
424.0ms	(- (* (- x 0.5) (log x)) x)
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	576	925
1	2275	825
2	5001	802

prune458.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (+ 0.91893853320467 (- x)) x))
0.2b	(fma (- x 0.5) (log x) (- (* x 1)))
3.6b	(+ (+ 0.91893853320467 (- x)) x)
3.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
25×	`add-log-exp`
16×	`distribute-lft-out`
14×	`add-sqr-sqrt` `add-cube-cbrt` `sum-log`
9×	`times-frac`
8×	`fma-def`
6×	`add-exp-log` `associate-+l-` `add-cbrt-cube`
5×	`associate-+r-`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-neg-in` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `neg-sub0` `associate-+l+` `unsub-neg` `neg-log` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `associate-+r+` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

109.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (+ 0.91893853320467 (- x)) x))
0.0ms	(fma (- x 0.5) (log x) (- (* x 1)))
51.0ms	(+ (+ 0.91893853320467 (- x)) x)
52.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series631.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(+ (fma (- x 0.5) (log x) (- (* x 1))) (+ (+ 0.91893853320467 (- x)) x))
276.0ms	(fma (- x 0.5) (log x) (- (* x 1)))
1.0ms	(+ (+ 0.91893853320467 (- x)) x)
81.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	482	812
1	2281	706
2	5003	673

prune429.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(+ (fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x))) x)
0.3b	(fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x)))
3.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

73.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
5.0ms	(+ (fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x))) x)
0.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x)))
66.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series746.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
304.0ms	(+ (fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x))) x)
295.0ms	(fma (log x) (- x 0.5) (- 0.91893853320467 (+ x x)))
108.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	472	779
1	1582	710
2	5003	708

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

regimes284.0ms

Accuracy

64.4% (1.0b remaining)

Error of 4.2b against oracle of 3.2b and baseline of 5.9b

bsearch60.0ms

Steps

Iters	Range		Point
6	35032751910769.78	141169876815523.12	139847743809662.47

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	47	29

end0.0ms

sample2.0s

Algorithm

intervals

Results

822.0ms	11762×	body	80	valid
520.0ms	11847×	body	80	nan