Details

sample108.0ms

Algorithm

intervals

Results

34.0ms	49×	body	1280	valid
18.0ms	47×	body	640	valid
10.0ms	113×	body	80	valid
10.0ms	36×	body	320	valid
7.0ms	59×	body	80	overflowed
4.0ms	72×	body	80	nan
3.0ms	3×	body	2560	valid
3.0ms	9×	body	640	nan
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	2×	body	160	nan

simplify203.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 24.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
0.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.7b	(+ (- 1.0 y) (* y (exp z)))

rewrite54.0ms

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))
23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
11.0ms	(log (+ (- 1.0 y) (* y (exp z))))
13.0ms	(+ (- 1.0 y) (* y (exp z)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* y (exp z))
154.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
75.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

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

prune271.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* y (exp z)))
0.7b	(cbrt (* y (exp z)))
1.9b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
12.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-cbrt-cube`
3×	`log-prod`
2×	`cbrt-prod` `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 → 47

Calls

4 calls:

3.0ms	(cbrt (* y (exp z)))
3.0ms	(cbrt (* y (exp z)))
17.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
17.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* y (exp z)))
57.0ms	(cbrt (* y (exp z)))
92.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
59.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	304	834
1	965	674
2	4340	577
3	5002	575

prune203.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
1.8b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
12.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
12.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite71.0ms

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:

16.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
16.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
20.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
17.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
157.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
51.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
56.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	284	1680
1	843	1416
2	3705	1300
3	5002	1276

prune372.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 3.8b

localize17.0ms

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))
3.8b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.0b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite33.0ms

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

series319.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 0.5 (pow z 2))
71.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
91.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
126.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify59.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (50.0ms)

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

prune480.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.8b

regimes447.0ms

Accuracy

72.5% (4.7b remaining)

Error of 9.4b against oracle of 4.8b and baseline of 21.8b

bsearch139.0ms

Steps

Iters	Range		Point
8	1.744684644555791e-189	1.4216327668891872e-185	5.139847785379201e-188
4	-113489.77514193834	-70386.57554482119	-71733.55053223111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	51
1	57	51

end0.0ms

sample3.2s

Algorithm

intervals

Results

997.0ms	1455×	body	1280	valid
622.0ms	1527×	body	640	valid
318.0ms	3587×	body	80	valid
257.0ms	952×	body	320	valid
155.0ms	2539×	body	80	nan
108.0ms	1534×	body	80	overflowed
105.0ms	76×	body	2560	valid
83.0ms	269×	body	640	nan
76.0ms	435×	body	160	valid
46.0ms	105×	body	1280	nan
42.0ms	195×	body	320	nan
15.0ms	109×	body	160	nan