Details

sample204.0ms

Algorithm

intervals

Results

89.0ms	1635×	body	80	nan
32.0ms	509×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.7b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.0b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite127.0ms

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:

12.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
31.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
77.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series388.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
122.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
168.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

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

prune424.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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

rewrite56.0ms

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:

35.0ms	(* 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)
13.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series833.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
82.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
80.0ms	(fma (log (/ 1 a)) t b)
328.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify92.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	904	2177
1	4141	1915
2	5001	1905

prune723.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (/ 1 a)) t b)
0.1b	(pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3)
1.0b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))))) y)
43.6b	(cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
16×	`div-exp`
14×	`add-cbrt-cube`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`prod-exp`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `pow-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `associate-/r*`
2×	`cube-mult` `pow-to-exp` `unpow3` `cbrt-unprod` `sqr-pow`
1×	`rec-exp` `pow-pow` `frac-2neg` `pow1/3` `1-exp` `associate-r/` `clear-num` `rem-cbrt-cube` `fma-udef` `div-inv` `associate-/l/` `associate-/l` `rem-cube-cbrt`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
1.0ms	(pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3)
27.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))))) y)
1.0ms	(cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))

series2.8s

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma (log (/ 1 a)) t b)
2.3s	(pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3)
340.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))))) y)
99.0ms	(cbrt (pow (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)) 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	594	1258
1	2569	1059
2	5002	1029

prune376.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 a))
0.1b	(fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
9.6b	(* (/ (pow (/ 1 (pow a 1.0)) 1.0) (exp (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)))) (/ x y))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
176×	`add-sqr-sqrt`
154×	`unpow-prod-down`
120×	`associate-l`
114×	`*-un-lft-identity`
108×	`add-cube-cbrt`
72×	`add-exp-log`
51×	`div-exp`
31×	`fma-udef`
29×	`exp-sum`
26×	`pow-exp` `prod-exp`
22×	`sqr-pow`
20×	`unswap-sqr`
16×	`add-cbrt-cube`
13×	`log-prod` `associate-r`
8×	`pow1` `pow-to-exp`
7×	`rec-exp` `1-exp` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `rem-log-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`log-pow`
1×	`frac-times` `log-div` `pow-flip` `associate-r/` `log-rec` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 248

Calls

4 calls:

2.0ms	(log (/ 1 a))
0.0ms	(fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
74.0ms	(* (/ (pow (/ 1 (pow a 1.0)) 1.0) (exp (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)))) (/ x y))

series795.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(log (/ 1 a))
94.0ms	(fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b))
73.0ms	(fma (log (/ 1 a)) t b)
512.0ms	(* (/ (pow (/ 1 (pow a 1.0)) 1.0) (exp (fma (log (/ 1 z)) y (fma (log (/ 1 a)) t b)))) (/ x y))

simplify106.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1393	3618
1	4444	3448
2	5002	3421

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes177.0ms

Accuracy

52.5% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 1.3b

bsearch307.0ms

Steps

Iters	Range		Point
8	3.3287878951861095e-224	7.255245196657817e-221	1.190356007915927e-222
8	-2.3832728625365243e-91	-1.7151445531670253e-95	-1.0216426453804218e-94

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	42	27

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	45972×	body	80	nan
930.0ms	15167×	body	80	valid