Details

sample103.0ms

Algorithm

intervals

Results

30.0ms	62×	body	10240	exit
19.0ms	35×	body	1280	valid
14.0ms	49×	body	640	valid
7.0ms	121×	body	80	valid
7.0ms	35×	body	320	valid
3.0ms	78×	body	80	nan
3.0ms	1×	body	2560	valid
2.0ms	17×	body	160	valid
1.0ms	7×	body	640	nan
1.0ms	5×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	3×	body	160	nan

simplify209.0ms

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: 23.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
3.1b	(+ (- 1.0 y) (* y (exp z)))

rewrite52.0ms

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)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
13.0ms	(+ (- 1.0 y) (* y (exp z)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
153.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
71.0ms	(log (+ (- 1.0 y) (* y (exp z))))
39.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (43.0ms)

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

prune280.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* y (exp z)))
0.7b	(cbrt (* y (exp z)))
3.6b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
11.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite42.0ms

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))))))
18.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (* y (exp z)))
61.0ms	(cbrt (* y (exp z)))
89.0ms	(log (+ (- 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)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (109.0ms)

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

prune216.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
11.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
11.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
11.2b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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)))))
18.0ms	(+ (- 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)))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
53.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
55.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
55.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify111.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	253	1312
1	830	1006
2	3829	787
3	5002	787

prune341.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

3.3b	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
5.3b	(/ (* z y) t)
5.7b	(* (pow z 2) y)
6.6b	(/ (* (pow z 2) y) t)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

34.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
3.0ms	(/ (* z y) t)
6.0ms	(* (pow z 2) y)
4.0ms	(/ (* (pow z 2) y) t)

series143.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
23.0ms	(/ (* z y) t)
17.0ms	(* (pow z 2) y)
19.0ms	(/ (* (pow z 2) y) t)

simplify73.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	493	659
1	2291	586
2	5001	586

prune295.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

regimes427.0ms

Accuracy

70.9% (5.1b remaining)

Error of 9.1b against oracle of 4.0b and baseline of 21.6b

bsearch145.0ms

Steps

Iters	Range		Point
7	5.951993071617296e-108	4.937911139442563e-106	1.538587682197149e-106
8	-2.940000499063486e-22	-5.1547036328891616e-26	-2.888739096585429e-22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	38
1	58	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

746.0ms	1499×	body	10240	exit
741.0ms	1419×	body	1280	valid
457.0ms	1589×	body	640	valid
216.0ms	3571×	body	80	valid
170.0ms	939×	body	320	valid
92.0ms	2510×	body	80	nan
81.0ms	61×	body	2560	valid
51.0ms	454×	body	160	valid
50.0ms	257×	body	640	nan
34.0ms	117×	body	1280	nan
27.0ms	208×	body	320	nan
9.0ms	107×	body	160	nan