Details

analyze935.0ms

Algorithm: search

sample113.0ms

Algorithm

intervals

Results

32.0ms	491×	body	80	nan
20.0ms	233×	body	80	invalid
20.0ms	256×	body	80	valid

simplify54.0ms

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

prune15.0ms

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: 0.2b

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))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.6b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

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))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series126.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (- t 1.0) (log a))
7.0ms	(* y (log z))
43.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
67.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify60.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	569	965
1	2353	793
2	5001	726

prune159.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
0.3b	(* (log (/ 1 z)) y)
0.3b	(* (log (/ 1 a)) t)
1.6b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
82×	`add-sqr-sqrt` `associate-r`
62×	`*-un-lft-identity`
61×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
15×	`associate-l`
14×	`pow1`
8×	`distribute-lft-neg-out` `log-rec` `pow-exp` `unswap-sqr`
6×	`log-pow` `cbrt-unprod` `div-inv`
5×	`cbrt-undiv` `sqr-pow`
4×	`exp-diff` `associate-/r/` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `associate-+r-` `rec-exp` `distribute-neg-out` `pow-flip` `1-exp` `associate-*r/` `unsub-neg` `inv-pow`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 177

Calls

4 calls:

28.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
5.0ms	(* (log (/ 1 z)) y)
4.0ms	(* (log (/ 1 a)) t)
18.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

series291.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))
11.0ms	(* (log (/ 1 z)) y)
10.0ms	(* (log (/ 1 a)) t)
136.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))) y)

simplify124.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1050	2460
1	4978	2167
2	5002	2167

prune489.0ms

Filtered

131 candidates to 189 candidates (-44.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	188	5	193

Merged error: 0.0b

Counts

193 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
0.3b	(* (log (/ 1 z)) y)
0.3b	(* (log (/ 1 a)) t)
1.2b	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

1197×	`times-frac`
542×	`add-sqr-sqrt`
514×	`*-un-lft-identity`
513×	`add-cube-cbrt`
367×	`unpow-prod-down`
238×	`associate-r`
119×	`exp-sum`
76×	`associate-/l*`
45×	`add-exp-log`
44×	`distribute-lft-neg-out` `log-rec`
37×	`div-inv`
30×	`div-exp`
29×	`sqr-pow`
28×	`exp-diff` `associate-/r/`
22×	`add-cbrt-cube`
15×	`associate-l`
14×	`pow1` `associate-+r-` `distribute-neg-out` `unsub-neg`
10×	`prod-exp`
9×	`unswap-sqr`
8×	`pow-exp`
6×	`cbrt-undiv` `log-pow`
5×	`cbrt-unprod`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `inv-pow`
1×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`

Counts

4 → 634

Calls

4 calls:

25.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
8.0ms	(* (log (/ 1 z)) y)
5.0ms	(* (log (/ 1 a)) t)
63.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

series279.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y)
12.0ms	(* (log (/ 1 z)) y)
11.0ms	(* (log (/ 1 a)) t)
133.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))) y))

simplify161.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2629	12265
1	5002	11836

prune2.7s

Filtered

471 candidates to 646 candidates (-37.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	645	1	646
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	646	5	651

Merged error: 0b

Counts

651 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
0.3b	(* (log (/ 1 z)) y)
0.3b	(* (log (/ 1 a)) t)
1.2b	(* x (/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

5218×	`times-frac`
2129×	`add-sqr-sqrt`
2075×	`*-un-lft-identity`
2066×	`add-cube-cbrt`
1098×	`unpow-prod-down`
710×	`associate-r`
357×	`exp-sum`
233×	`associate-/r*`
140×	`add-exp-log`
128×	`distribute-lft-neg-out` `log-rec`
122×	`div-exp`
114×	`div-inv`
93×	`associate-/r/`
86×	`sqr-pow`
84×	`exp-diff`
42×	`associate-+r-` `distribute-neg-out` `unsub-neg`
31×	`add-cbrt-cube`
27×	`prod-exp`
24×	`pow-exp`
22×	`rec-exp` `1-exp`
17×	`unswap-sqr`
15×	`pow1` `associate-l`
12×	`cbrt-undiv`
6×	`pow-to-exp` `log-pow` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-flip` `pow-prod-down` `-commutative` `associate-/l` `inv-pow`
1×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv`

Counts

4 → 1781

Calls

4 calls:

56.0ms	(/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
4.0ms	(* (log (/ 1 z)) y)
4.0ms	(* (log (/ 1 a)) t)
165.0ms	(* x (/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t)))))))
10.0ms	(* (log (/ 1 z)) y)
10.0ms	(* (log (/ 1 a)) t)
122.0ms	(* x (/ 1 (/ y (/ (pow (/ 1 a) 1.0) (exp (+ b (+ (* (log (/ 1 z)) y) (* (log (/ 1 a)) t))))))))

simplify404.0ms

Algorithm

egg-herbie

Counts

1793 → 1793

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5001	40366

prune16.1s

Filtered

1407 candidates to 1793 candidates (-27.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1792	1	1793
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	1793	5	1798

Merged error: 0b

Counts

1798 → 5

regimes602.0ms

Accuracy

94.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.3b

bsearch1.7s

Steps

Iters	Range		Point
8	3.23746749922709e-08	1.7260094748764025e-05	1.0194401551935762e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	29
1	35	29

end0.0ms

analyze821.0ms

Algorithm: search

sample3.0s

Algorithm

intervals

Results

935.0ms	14292×	body	80	nan
619.0ms	8000×	body	80	valid
537.0ms	7153×	body	80	invalid

Details

analyze935.0ms

sample113.0ms

simplify54.0ms

prune15.0ms

localize16.0ms

rewrite32.0ms

series126.0ms

simplify60.0ms

prune159.0ms

localize22.0ms

rewrite67.0ms

series291.0ms

simplify124.0ms

prune489.0ms

localize21.0ms

rewrite157.0ms

series279.0ms

simplify161.0ms

prune2.7s

localize20.0ms

rewrite442.0ms

series248.0ms

simplify404.0ms

prune16.1s

regimes602.0ms

bsearch1.7s

simplify2.0ms

end0.0ms

analyze821.0ms

sample3.0s

Profiling