Details

sample207.0ms

Algorithm

intervals

Results

90.0ms	1143×	body	80	nan
35.0ms	388×	body	80	valid
6.0ms	13×	body	640	valid
5.0ms	18×	body	320	valid
4.0ms	3×	body	1280	valid
1.0ms	7×	body	160	valid

simplify37.0ms

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: 0.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.3b	(log (- 1.0 z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series332.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (log z) t)
65.0ms	(* y (- (log z) t))
171.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
40.0ms	(log (- 1.0 z))

simplify62.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	593	882
1	2248	832
2	5001	830

prune339.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Merged error: 0.0b

Counts

119 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

21.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
4.0ms	(- (log z) t)
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)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
59.0ms	(- (log z) t)
69.0ms	(* 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)))

simplify71.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	580	1354
1	2377	1266
2	5001	1262

prune434.0ms

Filtered

115 candidates to 81 candidates (70.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	2	117

Merged error: 0.0b

Counts

117 → 2

localize25.0ms

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	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

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))
22.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
8.0ms	(* 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)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(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))
308.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
66.0ms	(* y (- (log z) t))
232.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify91.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	675	2264
1	2911	2128
2	5001	2113

prune508.0ms

Filtered

135 candidates to 86 candidates (63.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))
0.1b	(* y (- (log z) t))
0.2b	(* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

5.0ms	(exp (* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))
7.0ms	(* y (- (log z) t))
11.0ms	(* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
22.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(exp (* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))
66.0ms	(* y (- (log z) t))
262.0ms	(* (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
230.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify90.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	659	1890
1	2784	1743
2	5001	1723

prune499.0ms

Filtered

120 candidates to 85 candidates (70.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

regimes372.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.1s	40752×	body	80	nan
1.0s	12453×	body	80	valid
173.0ms	393×	body	640	valid
110.0ms	399×	body	320	valid
62.0ms	74×	body	1280	valid
49.0ms	282×	body	160	valid

Details

sample207.0ms

simplify37.0ms

prune3.0ms

localize15.0ms

rewrite31.0ms

series332.0ms

simplify62.0ms

prune339.0ms

localize23.0ms

rewrite55.0ms

series525.0ms

simplify71.0ms

prune434.0ms

localize25.0ms

rewrite71.0ms

series769.0ms

simplify91.0ms

prune508.0ms

localize25.0ms

rewrite50.0ms

series735.0ms

simplify90.0ms

prune499.0ms

regimes372.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling