Details

sample183.0ms

Algorithm

intervals

Results

75.0ms	1468×	body	80	nan
31.0ms	515×	body	80	valid

simplify62.0ms

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

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.5b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
84×	`times-frac` `associate-r`
80×	`exp-sum`
74×	`add-cube-cbrt`
72×	`log-prod`
70×	`associate--l+`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+` `associate-+r+`
28×	`associate-/l*`
27×	`associate-l`
15×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`exp-prod`
10×	`pow1` `distribute-lft-out--` `add-log-exp`
6×	`*-commutative` `distribute-lft-out` `unswap-sqr`
5×	`+-commutative` `sub-neg`
4×	`prod-exp`
3×	`div-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `pow-prod-down` `associate-*l/` `log-pow` `difference-of-squares`
1×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
37.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
28.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series391.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- t 1.0) (log a))
38.0ms	(* y (log z))
171.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
121.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify117.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1036	2693
1	3948	2303
2	5001	2275

prune557.0ms

Filtered

235 candidates to 155 candidates (34.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	227	8	235
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	8	237

Merged error: 0.0b

Counts

237 → 8

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

rewrite795.0ms

Algorithm

rewrite-expression-head

Rules

7657×	`times-frac`
3327×	`add-sqr-sqrt`
3262×	`*-un-lft-identity`
3255×	`add-cube-cbrt`
2610×	`exp-sum`
2288×	`log-prod`
2269×	`associate-r`
2262×	`associate-+l+`
2183×	`unpow-prod-down`
1144×	`distribute-rgt-in` `distribute-lft-in`
616×	`associate-/l*`
349×	`div-inv`
174×	`+-commutative` `associate-+r+`
171×	`sqr-pow`
73×	`add-exp-log`
69×	`associate-/r*`
55×	`associate-/l/`
53×	`associate-*r/`
46×	`div-exp`
26×	`unswap-sqr`
21×	`associate-l`
19×	`add-cbrt-cube`
16×	`pow-exp`
15×	`prod-exp`
12×	`pow1`
6×	`log-rec` `clear-num` `log-pow` `*-commutative`
5×	`cbrt-undiv`
4×	`pow-to-exp` `rec-exp` `1-exp` `cbrt-unprod` `add-log-exp`
3×	`distribute-lft-neg-out` `frac-2neg` `distribute-rgt-neg-out`
2×	`pow-flip` `pow-prod-down` `un-div-inv` `inv-pow`

Counts

4 → 3109

Calls

4 calls:

52.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
250.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series730.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
63.0ms	(* (log (/ 1 a)) t)
39.0ms	(* y (log (/ 1 z)))
339.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify720.0ms

Algorithm

egg-herbie

Counts

3121 → 3121

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5046	75922

prune17.3s

Filtered

3121 candidates to 2765 candidates (11.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	3118	3	3121
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	3122	7	3129

Merged error: 0.0b

Counts

3129 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
0.6b	(cbrt z)
0.6b	(cbrt z)
0.9b	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

310×	`associate-+l+`
240×	`exp-sum`
230×	`associate--l+`
214×	`*-un-lft-identity`
210×	`log-prod`
204×	`associate-r`
180×	`times-frac`
165×	`distribute-rgt-in` `distribute-lft-in`
160×	`add-sqr-sqrt`
150×	`add-cube-cbrt`
96×	`cbrt-prod`
90×	`associate-+r+`
60×	`associate-/l*`
34×	`associate-l`
27×	`distribute-lft-out`
21×	`distribute-lft-out--`
20×	`exp-prod`
14×	`add-log-exp`
11×	`add-exp-log`
10×	`+-commutative`
9×	`add-cbrt-cube`
5×	`sub-neg`
4×	`pow1` `*-commutative` `rem-exp-log` `unswap-sqr`
3×	`diff-log` `div-exp` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `exp-diff` `pow1/3` `prod-exp`
1×	`frac-2neg` `associate-*r/` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `difference-of-squares`

Counts

4 → 361

Calls

4 calls:

93.0ms	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
1.0ms	(cbrt z)
1.0ms	(cbrt z)
69.0ms	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

series807.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (* x (exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))) y)
187.0ms	(cbrt z)
177.0ms	(cbrt z)
175.0ms	(exp (- (+ (+ (* y (* 2 (log (cbrt z)))) (* y (log (cbrt z)))) (* (- t 1.0) (log a))) b))

simplify101.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1925	7105
1	5001	6244

prune1.1s

Filtered

373 candidates to 227 candidates (39.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	372	1	373
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	373	7	380

Merged error: 0.0b

Counts

380 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ (cbrt 1) z)) y)
1.5b	(/ (* x (/ (pow (/ 1 1) 1.0) (exp (* (log (/ (* (cbrt 1) (cbrt 1)) 1)) y)))) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))))

rewrite7.3s

Algorithm

rewrite-expression-head

Rules

134971×	`times-frac`
53269×	`add-sqr-sqrt`
46852×	`*-un-lft-identity`
44443×	`add-cube-cbrt`
39302×	`unpow-prod-down`
23264×	`associate-r`
15740×	`exp-sum`
7870×	`+-commutative` `associate-+r+`
3573×	`div-inv`
3357×	`associate-/r/`
3270×	`sqr-pow`
3210×	`unswap-sqr`
2191×	`associate-/l*`
1614×	`associate-l`
1302×	`add-exp-log`
1240×	`div-exp`
1208×	`distribute-lft-neg-out` `log-rec`
1203×	`exp-neg`
1058×	`associate-/r*`
483×	`clear-num`
403×	`*-commutative`
364×	`pow-exp`
268×	`prod-exp`
182×	`1-exp`
98×	`rec-exp`
79×	`frac-2neg`
70×	`pow-to-exp`
46×	`add-cbrt-cube`
25×	`associate-/l/`
23×	`associate-*r/`
22×	`cbrt-undiv`
11×	`pow1`
8×	`cbrt-unprod`
4×	`log-pow` `add-log-exp`
2×	`pow-prod-down` `un-div-inv`
1×	`pow-flip` `inv-pow`

Counts

4 → 30738

Calls

4 calls:

35.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
6.0ms	(* (log (/ (cbrt 1) z)) y)
775.0ms	(/ (* x (/ (pow (/ 1 1) 1.0) (exp (* (log (/ (* (cbrt 1) (cbrt 1)) 1)) y)))) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))))

series790.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))
64.0ms	(* (log (/ 1 a)) t)
64.0ms	(* (log (/ (cbrt 1) z)) y)
366.0ms	(/ (* x (/ (pow (/ 1 1) 1.0) (exp (* (log (/ (* (cbrt 1) (cbrt 1)) 1)) y)))) (/ y (/ (pow (/ 1 a) 1.0) (exp (+ (* (log (/ (cbrt 1) z)) y) (+ (* (log (/ 1 a)) t) b))))))

simplify15.1s

Algorithm

egg-herbie

Counts

30750 → 30750

Iterations

Useful iterations: 0 (1.1s)

Iter	Nodes	Cost
0	46978	1577555

prune3.8m

Filtered

30750 candidates to 23445 candidates (23.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	30750	0	30750
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	30750	7	30757

Merged error: 0.0b

Counts

30757 → 7

regimes460.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	46016×	body	80	nan
939.0ms	15367×	body	80	valid