Details

sample181.0ms

Algorithm

intervals

Results

72.0ms	1417×	body	80	nan
33.0ms	469×	body	80	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.5b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

12.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
83.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
37.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series389.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
174.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
120.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune373.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
0.5b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
96×	`add-sqr-sqrt`
81×	`associate-r`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
14×	`pow1`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-l`
8×	`pow-exp` `div-inv` `unswap-sqr`
6×	`log-pow` `cbrt-unprod`
5×	`cbrt-undiv` `sqr-pow`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-*r/` `log-rec` `inv-pow`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `distribute-rgt-neg-out` `associate-/l/` `associate-/l*`

Counts

4 → 199

Calls

4 calls:

159.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
8.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
104.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series977.0ms

Counts

4 → 12

Calls

4 calls:

528.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
38.0ms	(* y (log (/ 1 z)))
63.0ms	(* (log (/ 1 a)) t)
347.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify47.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune801.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.5b	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

607×	`add-exp-log`
323×	`div-exp`
234×	`prod-exp`
112×	`pow-exp`
44×	`add-cbrt-cube`
28×	`pow-to-exp` `rec-exp` `1-exp`
19×	`cbrt-unprod`
18×	`add-sqr-sqrt` `associate-l`
17×	`cbrt-undiv`
16×	`pow1`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r` `log-pow`
4×	`add-log-exp`
3×	`distribute-lft-neg-out` `pow-flip` `times-frac` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 194

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
335.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

series769.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (log (/ 1 a)) t)
62.0ms	(* (log (/ 1 a)) t)
57.0ms	(* (log (/ 1 a)) t)
588.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ (pow (/ 1 (sqrt a)) 1.0) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

simplify112.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	1245	5860
1	3649	5044
2	5001	4831

prune603.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 a)) t)
0.5b	(/ (* (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) x) y)
0.5b	(pow (/ 1 (sqrt a)) (* 2 1.0))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log`
46×	`div-exp`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
22×	`unpow-prod-down` `prod-exp`
21×	`times-frac`
15×	`pow1`
12×	`associate-l` `pow-exp`
10×	`cbrt-undiv`
9×	`sqrt-prod`
7×	`cbrt-unprod`
6×	`associate-r` `log-pow`
5×	`pow-flip` `pow-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-/r*` `inv-pow`
2×	`distribute-lft-neg-out` `log-rec` `pow-prod-down` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow-unpow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `clear-num` `associate-/l/` `associate-/l` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
5.0ms	(* (log (/ 1 a)) t)
125.0ms	(/ (* (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) x) y)
7.0ms	(pow (/ 1 (sqrt a)) (* 2 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (log (/ 1 a)) t)
62.0ms	(* (log (/ 1 a)) t)
889.0ms	(/ (* (/ (/ (pow (/ 1 (sqrt a)) (* 2 1.0)) (* (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) x) y)
121.0ms	(pow (/ 1 (sqrt a)) (* 2 1.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	900	2512
1	3470	1581
2	5003	1440

prune576.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	37
1	35	37
2	35	37

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	44143×	body	80	nan
903.0ms	14865×	body	80	valid