Details

sample109.0ms

Algorithm

intervals

Results

27.0ms	51×	body	10240	exit
25.0ms	43×	body	1280	valid
15.0ms	52×	body	640	valid
7.0ms	114×	body	80	valid
5.0ms	29×	body	320	valid
4.0ms	99×	body	80	nan
3.0ms	1×	body	2560	valid
2.0ms	11×	body	640	nan
2.0ms	18×	body	160	valid
1.0ms	7×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	2×	body	160	nan

simplify210.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	710	7
9	1092	7
10	1240	7
11	1558	7
12	4191	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
3.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* y (exp z))
22.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
13.0ms	(+ (- 1.0 y) (* y (exp z)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
149.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
69.0ms	(log (+ (- 1.0 y) (* y (exp z))))
37.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5001	726

prune256.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.4b	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`log-prod`
2×	`log-div` `associate-+l+` `flip3-+` `pow1/3` `sum-log` `flip-+`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 51

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
11.0ms	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
15.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt y)
181.0ms	(cbrt y)
93.0ms	(log (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z)))))
56.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

simplify38.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	289	602
1	1035	526
2	5001	488

prune222.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
13.9b	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`log-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod`
4×	`log-div` `associate-+l+` `cbrt-div` `flip3-+` `sum-log` `log-pow` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `associate-+l-` `sub-neg` `pow1/3` `diff-log` `rem-log-exp`

Counts

4 → 66

Calls

4 calls:

14.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
12.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
15.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
15.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
164.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))))
60.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))
54.0ms	(+ (- 1.0 y) (* (* (cbrt y) (cbrt y)) (* (cbrt y) (exp z))))

simplify147.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	291	1264
1	964	1148
2	4690	1072
3	5001	1032

prune379.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
4.3b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.1b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-r`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* 0.5 (pow z 2))
3.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
14.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
11.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series317.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow z 2))
73.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
91.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
127.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	415	800
1	1832	721
2	5001	715

prune297.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.8b

regimes421.0ms

Accuracy

73.6% (4.4b remaining)

Error of 9.1b against oracle of 4.7b and baseline of 21.5b

bsearch119.0ms

Steps

Iters	Range		Point
5	4.2185849944799077e-221	9.771091612138487e-221	9.274120679861768e-221
7	-91.73841076085421	-0.49115008736797033	-0.4984438493979181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	29
1	52	29

end0.0ms

sample3.1s

Algorithm

intervals

Results

779.0ms	1451×	body	1280	valid
751.0ms	1483×	body	10240	exit
452.0ms	1536×	body	640	valid
215.0ms	3588×	body	80	valid
166.0ms	886×	body	320	valid
92.0ms	2409×	body	80	nan
88.0ms	66×	body	2560	valid
59.0ms	500×	body	160	valid
52.0ms	259×	body	640	nan
35.0ms	112×	body	1280	nan
31.0ms	196×	body	320	nan
9.0ms	113×	body	160	nan