Details

sample180.0ms

Algorithm

intervals

Results

74.0ms	1461×	body	80	nan
28.0ms	463×	body	80	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite32.0ms

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:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series373.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- t 1.0) (log a))
39.0ms	(* y (log z))
164.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
115.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify60.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (51.0ms)

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

prune365.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
0.9b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite71.0ms

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:

27.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
4.0ms	(* (log (/ 1 a)) t)
9.0ms	(* y (log (/ 1 z)))
20.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series774.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
62.0ms	(* (log (/ 1 a)) t)
38.0ms	(* y (log (/ 1 z)))
336.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify57.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune829.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
0.3b	(* y (log (/ 1 z)))
0.9b	(/ (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

319×	`add-exp-log`
177×	`div-exp`
108×	`prod-exp`
60×	`pow-exp`
52×	`log-prod`
46×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
39×	`times-frac` `add-cbrt-cube`
26×	`distribute-rgt-in` `distribute-lft-in`
16×	`pow1`
15×	`pow-to-exp` `rec-exp` `1-exp` `associate-r`
13×	`cbrt-unprod`
12×	`cbrt-undiv` `associate-l`
9×	`log-pow`
5×	`div-inv`
4×	`add-log-exp`
3×	`pow-flip` `associate-r/` `log-rec` `pow-prod-down` `associate-/r` `*-commutative` `associate-/l/` `inv-pow` `unswap-sqr`
2×	`distribute-rgt-neg-out`
1×	`distribute-lft-neg-out` `frac-times` `frac-2neg` `associate-l/` `clear-num` `associate-/l`

Counts

4 → 202

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
11.0ms	(* y (log (/ 1 z)))
7.0ms	(* y (log (/ 1 z)))
46.0ms	(/ (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

series482.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (log (/ 1 a)) t)
38.0ms	(* y (log (/ 1 z)))
42.0ms	(* y (log (/ 1 z)))
338.0ms	(/ (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)

simplify109.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1033	3886
1	3741	2602
2	5003	2391

prune710.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
0.3b	(* y (log (/ 1 z)))
0.4b	(* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
441×	`add-sqr-sqrt`
435×	`add-cube-cbrt` `*-un-lft-identity`
388×	`associate-r`
346×	`add-exp-log`
273×	`unpow-prod-down`
204×	`sqrt-prod`
184×	`div-exp`
123×	`prod-exp`
64×	`pow-exp`
52×	`log-prod`
51×	`exp-sum`
46×	`add-cbrt-cube`
29×	`div-inv`
26×	`distribute-rgt-in` `distribute-lft-in`
21×	`pow1` `sqr-pow`
18×	`cbrt-unprod`
16×	`pow-to-exp` `rec-exp` `1-exp`
13×	`associate-l`
12×	`cbrt-undiv`
9×	`log-pow`
6×	`pow-prod-down`
4×	`*-commutative` `add-log-exp`
3×	`pow-flip` `associate-*r/` `log-rec` `inv-pow` `unswap-sqr`
2×	`distribute-rgt-neg-out`
1×	`distribute-lft-neg-out` `frac-times` `associate-*l/`

Counts

4 → 578

Calls

4 calls:

4.0ms	(* (log (/ 1 a)) t)
6.0ms	(* y (log (/ 1 z)))
7.0ms	(* y (log (/ 1 z)))
101.0ms	(* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

series489.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (log (/ 1 a)) t)
43.0ms	(* y (log (/ 1 z)))
38.0ms	(* y (log (/ 1 z)))
347.0ms	(* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (/ (pow (/ 1 a) (/ 1.0 2)) (sqrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))

simplify204.0ms

Algorithm

egg-herbie

Counts

590 → 590

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3560	16132
1	5001	15606

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes295.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	72
1	44	72

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	45345×	body	80	nan
948.0ms	15161×	body	80	valid