Details

sample255.0ms

Algorithm

intervals

Results

118.0ms	1546×	body	80	nan
52.0ms	529×	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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.8b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.2b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite132.0ms

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:

11.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
80.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
33.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series390.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- t 1.0) (log a))
41.0ms	(* y (log z))
172.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
122.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify57.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (46.0ms)

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

prune360.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.2b	(* y (log (/ 1 z)))
0.2b	(* (log (/ 1 a)) t)
0.8b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
86×	`add-sqr-sqrt`
82×	`add-cube-cbrt` `*-un-lft-identity`
65×	`unpow-prod-down`
37×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
19×	`add-cbrt-cube`
18×	`exp-sum` `associate-/l*`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
9×	`associate-r` `associate-l` `prod-exp` `div-inv`
8×	`pow-exp`
7×	`associate-/r*`
6×	`log-pow`
5×	`cbrt-undiv` `sqr-pow`
4×	`cbrt-unprod` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `log-rec` `pow-prod-down` `clear-num` `*-commutative` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-*r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

56.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
9.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
100.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series733.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
38.0ms	(* y (log (/ 1 z)))
62.0ms	(* (log (/ 1 a)) t)
345.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify105.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	922	3387
1	3977	2970
2	5002	2953

prune779.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.2b	(* y (log (/ 1 z)))
0.2b	(* (log (/ 1 a)) t)
0.8b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ 1 y))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
114×	`add-exp-log`
91×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
65×	`unpow-prod-down`
62×	`prod-exp`
56×	`div-exp`
31×	`add-cbrt-cube`
26×	`log-prod`
22×	`associate-r`
20×	`pow-exp`
18×	`exp-sum`
17×	`pow1` `associate-/l*`
13×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp`
12×	`cbrt-unprod`
10×	`associate-l`
9×	`div-inv`
6×	`cbrt-undiv` `log-pow`
5×	`pow-to-exp` `pow-prod-down` `sqr-pow`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r/` `-commutative`
2×	`pow-flip` `log-rec` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `frac-times` `frac-2neg` `associate-*l/` `clear-num` `un-div-inv` `distribute-rgt-neg-out`

Counts

4 → 242

Calls

4 calls:

58.0ms	(/ (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)
390.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ 1 y))

series746.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
43.0ms	(* y (log (/ 1 z)))
63.0ms	(* (log (/ 1 a)) t)
345.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) (/ 1 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1138	4065
1	5001	3533

prune867.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (/ 1 a) 1.0))
0.6b	(cbrt (pow (/ 1 a) 1.0))
0.6b	(cbrt (pow (/ 1 a) 1.0))
0.8b	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 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)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ 1 y))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

280×	`add-exp-log`
164×	`prod-exp`
96×	`add-cbrt-cube`
82×	`cbrt-unprod`
76×	`div-exp`
51×	`cbrt-prod`
39×	`unpow-prod-down`
38×	`cbrt-undiv`
36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `associate-r`
12×	`rec-exp` `1-exp`
9×	`associate-*r/`
6×	`pow-prod-down`
5×	`frac-times` `associate-*l/`
4×	`div-inv` `add-log-exp`
3×	`pow1/3` `sqr-pow`
1×	`associate-l` `un-div-inv` `*-commutative`

Counts

4 → 180

Calls

4 calls:

3.0ms	(cbrt (pow (/ 1 a) 1.0))
3.0ms	(cbrt (pow (/ 1 a) 1.0))
3.0ms	(cbrt (pow (/ 1 a) 1.0))
1.8s	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 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)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ 1 y))

series1.5s

Counts

4 → 12

Calls

4 calls:

370.0ms	(cbrt (pow (/ 1 a) 1.0))
362.0ms	(cbrt (pow (/ 1 a) 1.0))
370.0ms	(cbrt (pow (/ 1 a) 1.0))
353.0ms	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 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)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) (/ 1 y))

simplify71.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1258	6642
1	5002	4110

prune800.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (1.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.4s	45587×	body	80	nan
1.5s	15220×	body	80	valid