Details

sample209.0ms

Algorithm

intervals

Results

100.0ms	1539×	body	80	nan
35.0ms	469×	body	80	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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)

	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))
0.2b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.9b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite30.0ms

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))
6.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series373.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
115.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
164.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (43.0ms)

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

prune306.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Merged error: 0.0b

Counts

109 → 5

localize19.0ms

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)))))
0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.9b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite84.0ms

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:

30.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
11.0ms	(* y (log (/ 1 z)))
7.0ms	(* (log (/ 1 a)) t)
26.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series765.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
41.0ms	(* y (log (/ 1 z)))
58.0ms	(* (log (/ 1 a)) t)
327.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify51.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune708.0ms

Filtered

211 candidates to 145 candidates (68.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	207	4	211
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	211	5	216

Merged error: 0.0b

Counts

216 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.9b	(/ (cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3)) y)
2.9b	(cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
47×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
40×	`cbrt-prod`
26×	`log-prod`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
11×	`associate-/l*`
10×	`add-exp-log`
9×	`associate-r` `associate-l` `add-cbrt-cube`
6×	`log-pow`
5×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`cube-div` `cbrt-div` `pow-flip` `associate-r/` `log-rec` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`cbrt-undiv` `distribute-lft-neg-out` `frac-2neg` `pow1/3` `div-exp` `clear-num` `distribute-rgt-neg-out` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 148

Calls

4 calls:

9.0ms	(* y (log (/ 1 z)))
4.0ms	(* (log (/ 1 a)) t)
5.0ms	(/ (cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3)) y)
2.0ms	(cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3))

series808.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (log (/ 1 z)))
59.0ms	(* (log (/ 1 a)) t)
376.0ms	(/ (cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3)) y)
333.0ms	(cbrt (pow (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	615	2511
1	2427	2315
2	5002	2250

prune553.0ms

Filtered

160 candidates to 111 candidates (69.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	160	5	165

Merged error: 0.0b

Counts

165 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
0.2b	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
0.3b	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))
0.3b	(* (log (/ 1 a)) t)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
313×	`add-exp-log`
224×	`div-exp`
140×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
123×	`add-cube-cbrt` `prod-exp`
108×	`pow-exp`
107×	`unpow-prod-down`
87×	`associate-r`
31×	`add-cbrt-cube`
27×	`pow-to-exp` `rec-exp` `1-exp`
21×	`associate-/l*`
17×	`div-inv`
13×	`associate-l`
10×	`pow1` `cbrt-undiv`
9×	`sqr-pow`
8×	`cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `log-pow` `-commutative`
2×	`pow-prod-down`
1×	`distribute-lft-neg-out` `pow-flip` `frac-2neg` `associate-*r/` `exp-sum` `log-rec` `clear-num` `associate-/l/` `inv-pow`

Counts

4 → 337

Calls

4 calls:

21.0ms	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
16.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
33.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))
4.0ms	(* (log (/ 1 a)) t)

series867.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y)
120.0ms	(* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))
344.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (* (exp (+ (* (log (/ 1 a)) t) b)) (pow (/ 1 z) y))) y))
63.0ms	(* (log (/ 1 a)) t)

simplify71.0ms

Algorithm

egg-herbie

Counts

349 → 349

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1581	4899
1	5002	4441

prune937.0ms

Filtered

349 candidates to 206 candidates (59.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	348	6	354

Merged error: 0b

Counts

354 → 6

regimes345.0ms

Accuracy

84.7% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 5.4b

bsearch345.0ms

Steps

Iters	Range		Point
8	3.3490926414481955e-38	3.4331572961751836e-35	3.386130322081096e-35
7	-7581797934.7845745	-279124593.6259902	-284079592.0685607

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	48
1	54	48

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.0s	45707×	body	80	nan
1.2s	15256×	body	80	valid