Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	384×	body	80	valid
18.0ms	387×	body	80	nan

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

localize20.0ms

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)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite51.0ms

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:

10.0ms	(* (+ y 0.0007936500793651) z)
19.0ms	(* (- (* (+ 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)))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series273.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ y 0.0007936500793651) z)
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
123.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
84.0ms	(/ (+ (* (- (* (+ 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	446	778
1	1546	696
2	5002	694

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (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)
0.1b	(* (log x) (- x 0.5))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
101×	`prod-diff`
88×	`add-cube-cbrt`
68×	`associate-+r+`
54×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`add-log-exp`
10×	`add-exp-log` `flip3--` `associate-*r/` `add-cbrt-cube` `flip--`
9×	`pow1`
8×	`associate-r` `frac-add`
7×	`associate-l`
6×	`div-inv`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `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-` `fma-def` `frac-2neg` `div-exp` `clear-num` `log-pow` `associate--r-`

Counts

4 → 215

Calls

4 calls:

130.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
14.0ms	(* (log x) (- x 0.5))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series514.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
45.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
251.0ms	(* (log x) (- x 0.5))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify143.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1253	3523
1	4882	3081
2	5001	3081

prune793.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (log x) x) (* (log 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)
0.2b	(* (log x) x)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

134.0ms	(+ (+ (* (log x) x) (* (log x) (- 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
21.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
3.0ms	(* (log x) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series440.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ (+ (* (log x) x) (* (log x) (- 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
37.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
176.0ms	(* (log x) x)
88.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify142.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1196	3334
1	4957	2977
2	5001	2977

prune720.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x) x)
0.2b	(* (log x) x)
0.3b	(fma (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

3.0ms	(* (log x) x)
3.0ms	(* (log x) x)
0.0ms	(fma (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series921.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (log x) x)
185.0ms	(* (log x) x)
459.0ms	(fma (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (sqrt (+ (* (log x) x) (* (log x) (- 0.5)))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify38.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	317	845
1	1046	727
2	5001	705

prune372.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes306.0ms

Accuracy

0% (2.1b remaining)

Error of 5.8b against oracle of 3.8b and baseline of 5.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	36	15
2	37	15
3	37	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

627.0ms	11662×	body	80	valid
549.0ms	11506×	body	80	nan