Details

sample69.0ms

Algorithm

intervals

Results

24.0ms	390×	body	80	valid
20.0ms	425×	body	80	nan

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

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: 7.6b

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)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite51.0ms

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:

19.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
15.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series347.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
127.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
90.0ms	(/ (+ (* (- (* (+ 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

prune546.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series288.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ y 0.0007936500793651) z)
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
126.0ms	(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
88.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	444	778
1	1548	696
2	5001	694

prune362.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* (log x) (- x 0.5)) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
0.2b	(* (log x) (- x 0.5))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
24.0ms	(+ (* (log x) (- x 0.5)) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
7.0ms	(* (log x) (- x 0.5))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series542.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
140.0ms	(+ (* (log x) (- x 0.5)) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467))
274.0ms	(* (log x) (- x 0.5))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify99.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	820	1835
1	3231	1548
2	5001	1545

prune576.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* x (log x)) (fma (- 0.5) (log x) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467)))
0.2b	(* x (log x))
7.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
5.0ms	(+ (* x (log x)) (fma (- 0.5) (log x) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467)))
4.0ms	(* x (log x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series468.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
146.0ms	(+ (* x (log x)) (fma (- 0.5) (log x) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) x) 0.91893853320467)))
190.0ms	(* x (log x))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	510	1032
1	1986	930
2	5001	912

prune451.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

regimes380.0ms

Accuracy

68% (0.9b remaining)

Error of 4.1b against oracle of 3.2b and baseline of 6.0b

bsearch58.0ms

Steps

Iters	Range		Point
6	1134421401047092.0	10140450095606194.0	4636713545035469.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	24
1	44	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

640.0ms	11727×	body	80	valid
549.0ms	11555×	body	80	nan