Details

sample108.0ms

Algorithm

intervals

Results

45.0ms	386×	body	80	valid
37.0ms	405×	body	80	nan

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (22.0ms)

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: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
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)))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite48.0ms

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:

5.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
19.0ms	(* (- (* (+ 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)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series311.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
143.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
96.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (47.0ms)

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

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333)
0.1b	(* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x) (- x 0.91893853320467)))
4.5b	(/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`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` `associate-/r` `associate-/l`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333)
3.0ms	(* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x) (- x 0.91893853320467)))
8.0ms	(/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x)

series343.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333)
45.0ms	(* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z)
157.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x) (- x 0.91893853320467)))
91.0ms	(/ (+ (* (fma (+ y 0.0007936500793651) z (- 0.0027777777777778)) z) 0.083333333333333) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	360	804
1	1122	728
2	5001	712

prune374.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize18.0ms

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))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite199.0ms

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:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
132.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series570.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
154.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
278.0ms	(* (log x) (- x 0.5))
96.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify165.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (33.0ms)

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

prune899.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* (log x) x) (fma (- 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
0.3b	(* (log x) x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
7×	`associate-l`
6×	`associate-r` `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 → 89

Calls

4 calls:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
3.0ms	(+ (* (log x) x) (fma (- 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
3.0ms	(* (log x) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series497.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
155.0ms	(+ (* (log x) x) (fma (- 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
199.0ms	(* (log x) x)
94.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	483	913
1	1709	823
2	5003	812

prune395.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.0b

regimes485.0ms

Accuracy

85.3% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 5.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	40
1	53	40

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	11711×	body	80	valid
1.1s	11803×	body	80	nan