Details

sample174.0ms

Algorithm

intervals

Results

74.0ms	1328×	body	80	nan
25.0ms	409×	body	80	valid
3.0ms	15×	body	320	valid
3.0ms	8×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

simplify39.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.2b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.0b	(log (- 1.0 z))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

52.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
13.0ms	(* y (- (log z) t))
13.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series445.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
69.0ms	(* y (- (log z) t))
180.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify74.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	675	1085
1	2723	1003
2	5001	985

prune422.0ms

Filtered

119 candidates to 88 candidates (73.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite843.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

309.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
415.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
12.0ms	(* y (- (log z) t))
101.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
101.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
72.0ms	(* y (- (log z) t))
235.0ms	(+ (* 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

141 → 141

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	677	1907
1	3019	1768
2	5001	1757

prune597.0ms

Filtered

141 candidates to 94 candidates (66.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

56×	`associate--l+`
36×	`log-prod`
34×	`distribute-rgt-in` `distribute-lft-in`
28×	`add-sqr-sqrt` `associate-+r+`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt` `associate-+l+` `associate-*r/`
16×	`sub-neg`
12×	`associate-r`
10×	`pow1` `flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`distribute-lft-out--`
2×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

12.0ms	(* y (- (log z) t))
12.0ms	(* y (- (log z) t))
99.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
99.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	494	2014
1	2047	1920
2	5003	1910

prune903.0ms

Filtered

156 candidates to 110 candidates (70.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series751.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt x) (cbrt x))
179.0ms	(cbrt x)
191.0ms	(cbrt x)
179.0ms	(cbrt x)

simplify88.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune439.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes202.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	34
1	35	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

911.0ms	16545×	body	80	nan
313.0ms	5017×	body	80	valid
51.0ms	148×	body	640	valid
37.0ms	179×	body	320	valid
22.0ms	30×	body	1280	valid
15.0ms	112×	body	160	valid