Details

sample107.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
22.0ms	45×	body	10240	exit
14.0ms	50×	body	640	valid
9.0ms	117×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	25×	body	320	valid
3.0ms	77×	body	80	nan
1.0ms	7×	body	640	nan
1.0ms	10×	body	160	valid
1.0ms	4×	body	320	nan
0.0ms	2×	body	1280	nan
0.0ms	3×	body	160	nan

simplify202.0ms

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: 25.6b

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)))

rewrite37.0ms

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:

9.0ms	(* y (exp z))
13.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
6.0ms	(+ (- 1.0 y) (* y (exp z)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
163.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
74.0ms	(log (+ (- 1.0 y) (* y (exp z))))
61.0ms	(+ (- 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

prune265.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.0b	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
4.5b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.8b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
3×	`flip3-+` `associate-r` `associate-l` `associate-/r` `flip-+` `associate-/l`
2×	`associate-*r/` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
8.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series387.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
122.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
82.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
117.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	402	953
1	1641	882
2	5001	876

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
5.5b	(/ (* z y) t)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

10.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)

series101.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
19.0ms	(/ (* z y) t)

simplify83.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	204	286
1	812	256
2	3760	256
3	5001	256

prune124.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
13×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`div-inv`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow1` `diff-log`
1×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `sum-log` `associate-/r/` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 86

Calls

2 calls:

12.0ms	(- x (+ (* 1.0 (/ z (/ t y))) (/ (log 1.0) t)))
6.0ms	(/ z (/ t y))

series133.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(- x (+ (* 1.0 (/ z (/ t y))) (/ (log 1.0) t)))
21.0ms	(/ z (/ t y))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	431	653
1	1704	618
2	5001	617

prune266.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.5b

regimes381.0ms

Accuracy

68.3% (4.1b remaining)

Error of 7.8b against oracle of 3.8b and baseline of 16.6b

bsearch72.0ms

Steps

Iters	Range		Point
9	-6.5683629049692506e-15	-6.468064663008395e-20	-1.3525978244617489e-15

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample3.2s

Algorithm

intervals

Results

776.0ms	1469×	body	1280	valid
771.0ms	1574×	body	10240	exit
460.0ms	1581×	body	640	valid
208.0ms	3513×	body	80	valid
165.0ms	901×	body	320	valid
120.0ms	95×	body	2560	valid
92.0ms	2488×	body	80	nan
51.0ms	261×	body	640	nan
51.0ms	460×	body	160	valid
30.0ms	184×	body	320	nan
29.0ms	101×	body	1280	nan
9.0ms	111×	body	160	nan