Details

sample182.0ms

Algorithm

intervals

Results

76.0ms	1310×	body	80	nan
25.0ms	403×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	1×	body	1280	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0b	(log (- 1.0 z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`pow1`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`frac-add` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `log-pow` `rem-exp-log`
1×	`+-commutative` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

8.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
7.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series417.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
67.0ms	(* y (- (log z) t))
175.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
45.0ms	(log (- 1.0 z))

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	630	971
1	2443	914
2	5001	902

prune408.0ms

Filtered

113 candidates to 84 candidates (74.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0.3b

Counts

114 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
56×	`unpow-prod-down`
50×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`associate--l+`
24×	`unpow2` `sqr-pow`
18×	`log-prod` `unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-+r+`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
10×	`associate-+l+`
9×	`pow1` `div-exp` `add-log-exp`
8×	`sub-neg`
6×	`pow-to-exp` `associate-l` `pow-exp`
5×	`flip3--` `flip--`
4×	`frac-add`
3×	`exp-prod` `cbrt-unprod`
2×	`pow-prod-down` `sum-log` `*-commutative` `rem-exp-log` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `exp-sum` `log-pow` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 195

Calls

4 calls:

19.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
7.0ms	(* y (- (log z) t))
20.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
165.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
72.0ms	(* y (- (log z) t))
231.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify125.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1062	1909
1	4620	1720
2	5002	1718

prune885.0ms

Filtered

207 candidates to 135 candidates (65.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	209	4	213

Merged error: 0.0b

Counts

213 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate--l+`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`add-cube-cbrt`
14×	`cbrt-prod` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`sub-neg`
7×	`pow1`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`unpow-prod-down` `cube-prod` `frac-add`
3×	`exp-prod` `associate-l` `exp-sum`
2×	`sum-log` `rem-exp-log` `distribute-lft-out--`
1×	`+-commutative` `cube-mult` `flip3-+` `pow1/3` `unpow3` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

16.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
19.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
7.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
164.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
72.0ms	(* y (- (log z) t))
236.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify87.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	624	1859
1	2577	1812
2	5003	1803

prune579.0ms

Filtered

120 candidates to 81 candidates (67.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3))
0.0b	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
0.0b	(pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3)
0.1b	(* y (- (log z) t))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`cbrt-prod`
8×	`pow1` `unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `log-prod` `exp-prod` `associate-r` `associate--l+`
5×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
4×	`pow-pow`
3×	`pow-unpow` `associate-l`
2×	`cube-mult` `sub-neg` `unpow3` `associate-*r/` `rem-exp-log` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

7.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3))
8.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
10.0ms	(pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3)
8.0ms	(* y (- (log z) t))

series410.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3))
93.0ms	(exp (+ (* y (- (log z) t)) (* (log 1.0) a)))
151.0ms	(pow (exp (+ (* y (- (log z) t)) (* (log 1.0) a))) 3)
73.0ms	(* y (- (log z) t))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	346	925
1	1358	831
2	5002	804

prune332.0ms

Filtered

109 candidates to 66 candidates (60.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	109	3	112

Merged error: 0.0b

Counts

112 → 3

regimes266.0ms

Accuracy

50.9% (7.8b remaining)

Error of 7.9b against oracle of 0.1b and baseline of 15.9b

bsearch303.0ms

Steps

Iters	Range		Point
8	1.9573688422997066e-75	1.1585193730600142e-72	1.0531849876054006e-72
7	-6.242119527127205e-102	-1.9207694837257182e-103	-5.891439152752392e-102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	21
1	66	21
2	78	21
3	88	21
4	88	21

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	41528×	body	80	nan
820.0ms	12572×	body	80	valid
137.0ms	379×	body	640	valid
89.0ms	405×	body	320	valid
59.0ms	80×	body	1280	valid
38.0ms	272×	body	160	valid