Details

sample192.0ms

Algorithm

intervals

Results

80.0ms	1577×	body	80	nan
28.0ms	483×	body	80	valid

simplify53.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

4.0ms	(* y (log z))
103.0ms	(* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
34.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
81.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series475.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* y (log z))
146.0ms	(* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
115.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
172.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify52.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	404	981
1	1795	794
2	5001	742

prune360.0ms

Filtered

100 candidates to 76 candidates (76.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite276.0ms

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:

5.0ms	(* (log (/ 1 a)) t)
8.0ms	(* y (log (/ 1 z)))
153.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
100.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series801.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (log (/ 1 a)) t)
42.0ms	(* y (log (/ 1 z)))
343.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
353.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify50.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune823.0ms

Filtered

211 candidates to 145 candidates (68.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
104×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
87×	`add-cube-cbrt`
74×	`associate-r`
55×	`unpow-prod-down`
49×	`add-exp-log`
28×	`div-exp`
24×	`sqrt-prod`
22×	`add-cbrt-cube`
17×	`exp-sum`
15×	`associate-/r*`
14×	`prod-exp`
10×	`pow1`
8×	`pow-exp` `div-inv`
7×	`cbrt-undiv` `associate-/l*`
6×	`pow-flip` `unswap-sqr`
5×	`sqr-pow`
4×	`rec-exp` `1-exp` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
2×	`pow-to-exp` `associate-+l-` `sqrt-pow1` `pow1/2` `exp-diff` `associate-*r/` `log-rec` `associate-/r/` `distribute-rgt-neg-out` `inv-pow`
1×	`unsub-neg` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 221

Calls

4 calls:

285.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b)))))
3.0ms	(/ 1 (sqrt z))
3.0ms	(/ 1 (sqrt z))
191.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b))))) y)

series1.1s

Counts

4 → 12

Calls

4 calls:

509.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b)))))
28.0ms	(/ 1 (sqrt z))
31.0ms	(/ 1 (sqrt z))
502.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify55.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1077	3640
1	5001	3065

prune997.0ms

Filtered

233 candidates to 153 candidates (65.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
126×	`add-exp-log`
109×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
92×	`add-cube-cbrt`
87×	`associate-r`
67×	`prod-exp`
60×	`div-exp`
55×	`unpow-prod-down`
34×	`add-cbrt-cube`
24×	`sqrt-prod`
20×	`pow-exp`
17×	`exp-sum`
15×	`pow1` `rec-exp` `1-exp`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv` `div-inv`
6×	`pow-flip` `associate-/l*` `unswap-sqr`
5×	`pow-to-exp` `sqr-pow`
4×	`associate-r/` `associate-l*` `pow-prod-down` `add-log-exp`
2×	`associate-+l-` `frac-2neg` `sqrt-pow1` `pow1/2` `exp-diff` `log-rec` `clear-num` `associate-/r/` `*-commutative` `distribute-rgt-neg-out` `inv-pow`
1×	`frac-times` `unsub-neg` `associate-*l/` `un-div-inv`

Counts

4 → 258

Calls

4 calls:

281.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b)))))
3.0ms	(/ 1 (sqrt z))
3.0ms	(/ 1 (sqrt z))
742.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b))))) (/ 1 y))

series1.1s

Counts

4 → 12

Calls

4 calls:

522.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b)))))
28.0ms	(/ 1 (sqrt z))
34.0ms	(/ 1 (sqrt z))
513.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (+ (+ (* y (log (/ 1 (sqrt z)))) (* y (log (/ 1 (sqrt z))))) (+ (* (log (/ 1 a)) t) b))))) (/ 1 y))

simplify65.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1287	4490
1	5001	3731

prune1.0s

Filtered

270 candidates to 159 candidates (58.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes254.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	44786×	body	80	nan
900.0ms	15048×	body	80	valid