Details

sample118.0ms

Algorithm

intervals

Results

31.0ms	64×	body	10240	exit
27.0ms	51×	body	1280	valid
15.0ms	51×	body	640	valid
6.0ms	110×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	28×	body	320	valid
4.0ms	12×	body	160	valid
3.0ms	95×	body	80	nan
1.0ms	7×	body	640	nan
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify206.0ms

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: 23.0b

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)
1.5b	(+ (- 1.0 y) (* y (exp z)))
2.4b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite55.0ms

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))
25.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
13.0ms	(+ (- 1.0 y) (* y (exp z)))
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
161.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
36.0ms	(+ (- 1.0 y) (* y (exp z)))
80.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify50.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

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

prune305.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.0b	(* 0.5 (pow z 2))
2.8b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.6b	(/ (+ (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:

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

series310.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
25.0ms	(* 0.5 (pow z 2))
89.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
123.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (50.0ms)

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

prune344.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

5.6b	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) t)
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

13.0ms	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) t)
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) t)
126.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
118.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
120.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	393	1729
1	1360	1591
2	5001	1474

prune466.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) (* (cbrt t) (cbrt t)))
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
9.6b	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`cbrt-div`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`times-frac` `pow1/3` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 62

Calls

4 calls:

12.0ms	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) (* (cbrt t) (cbrt t)))
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
3.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ (+ (log 1.0) (* y (* (* (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))))) (* (cbrt t) (cbrt t)))
122.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
122.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))
128.0ms	(cbrt (+ (* 0.5 (pow z 2)) (* 1.0 z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	449	1601
1	1627	1407
2	5002	1277

prune440.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 5.1b

regimes888.0ms

Accuracy

74% (4.3b remaining)

Error of 8.8b against oracle of 4.5b and baseline of 21.1b

bsearch78.0ms

Steps

Iters	Range		Point
9	-3.0563469276612825e+22	-4.633285680425691e+16	-4.701304184126357e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

770.0ms	1552×	body	10240	exit
759.0ms	1440×	body	1280	valid
458.0ms	1581×	body	640	valid
202.0ms	3486×	body	80	valid
174.0ms	946×	body	320	valid
134.0ms	106×	body	2560	valid
90.0ms	2566×	body	80	nan
52.0ms	268×	body	640	nan
50.0ms	459×	body	160	valid
33.0ms	111×	body	1280	nan
26.0ms	203×	body	320	nan
10.0ms	121×	body	160	nan