Details

sample206.0ms

Algorithm

intervals

Results

70.0ms	1501×	body	80	nan
33.0ms	495×	body	80	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8
done	5001	8

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.3b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `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 → 112

Calls

4 calls:

25.0ms	(* (- t 1.0) (log a))
9.0ms	(* y (log z))
79.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
183.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series410.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
124.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
187.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify60.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860
done	5002	860

prune422.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
1.3b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

52.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
25.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series904.0ms

Counts

4 → 12

Calls

4 calls:

368.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
91.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
83.0ms	(fma (log (/ 1 a)) t b)
362.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify92.0ms

Counts

165 → 165

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	904	2177
1	4142	1910
2	5001	1900
done	5001	1900

prune733.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
0.2b	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
1.2b	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
82×	`div-exp`
39×	`times-frac`
28×	`prod-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`pow-exp`
13×	`rec-exp` `1-exp`
12×	`cbrt-undiv`
9×	`associate-/r*`
6×	`associate-/r/` `div-inv` `associate-/l*`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `pow-to-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`pow-flip` `inv-pow`

Counts

4 → 132

Calls

4 calls:

0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
45.0ms	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
22.0ms	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

series926.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
80.0ms	(fma (log (/ 1 a)) t b)
385.0ms	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
373.0ms	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

simplify70.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	690	2149
1	2902	1832
2	5001	1722
done	5001	1722

prune457.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 z))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.2b	(fma (log (/ 1 a)) t b)
5.6b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

3058×	`times-frac`
1222×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
240×	`fma-udef`
238×	`exp-sum`
145×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
44×	`add-exp-log`
39×	`div-exp`
16×	`add-cbrt-cube`
13×	`log-prod` `associate-/r*`
8×	`cbrt-undiv` `pow-exp`
6×	`pow1`
4×	`expm1-log1p-u` `rem-log-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `log-pow`
2×	`pow-to-exp`
1×	`log-div` `pow-flip` `frac-2neg` `log-rec` `clear-num` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 1104

Calls

4 calls:

3.0ms	(log (/ 1 z))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
58.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series842.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(log (/ 1 z))
91.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
81.0ms	(fma (log (/ 1 a)) t b)
551.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify252.0ms

Counts

1116 → 1116

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5001	28974
done	5001	28974

prune6.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes252.0ms

Accuracy

37.7% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.9b

bsearch327.0ms

Steps

Iters	Range		Point
9	7.791696405648315e-78	9.376691559823527e-73	9.283546491991938e-73
7	-2.6682199102389765e-257	-7.901070486114423e-259	-2.2383633819607527e-257

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	57
1	44	57
done	44	57

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.2s	45622×	body	80	nan
867.0ms	15188×	body	80	valid