Details

sample184.0ms

Algorithm

intervals

Results

75.0ms	1417×	body	80	nan
31.0ms	469×	body	80	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.5b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite137.0ms

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:

11.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
83.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
35.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series384.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
164.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
121.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

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

prune428.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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

rewrite65.0ms

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:

37.0ms	(* 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)
14.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series1.0s

Counts

4 → 12

Calls

4 calls:

338.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
275.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
82.0ms	(fma (log (/ 1 a)) t b)
335.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify104.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (79.0ms)

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

prune730.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
0.5b	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
41×	`div-exp`
26×	`add-cbrt-cube`
20×	`prod-exp`
14×	`cbrt-undiv`
8×	`cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `times-frac` `associate-/r*` `fma-udef` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
36.0ms	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series575.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma (log (/ 1 a)) t b)
80.0ms	(fma (log (/ 1 a)) t b)
78.0ms	(fma (log (/ 1 a)) t b)
336.0ms	(/ (* (/ x (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ (sqrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify69.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	543	1971
1	2281	1548
2	5001	1447

prune448.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (/ 1 a)) t b)
0.2b	(/ 1 (sqrt a))
0.2b	(/ (sqrt 1) (sqrt a))
0.5b	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ (sqrt 1) (sqrt a)) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

433×	`add-exp-log`
224×	`div-exp`
165×	`prod-exp`
68×	`pow-exp`
57×	`times-frac`
54×	`sqrt-prod`
49×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`add-cbrt-cube`
24×	`pow-to-exp`
19×	`cbrt-undiv`
16×	`cbrt-unprod`
15×	`associate-/r*`
11×	`rec-exp` `1-exp`
10×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `div-inv` `associate-/l/`
1×	`frac-times` `sqrt-undiv` `sqrt-pow1` `pow1/2` `associate-*l/` `fma-udef` `inv-pow`

Counts

4 → 222

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
3.0ms	(/ 1 (sqrt a))
4.0ms	(/ (sqrt 1) (sqrt a))
107.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ (sqrt 1) (sqrt a)) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series708.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma (log (/ 1 a)) t b)
33.0ms	(/ 1 (sqrt a))
28.0ms	(/ (sqrt 1) (sqrt a))
566.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ (sqrt 1) (sqrt a)) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify129.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1266	4951
1	4502	4105
2	5001	4029

prune810.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	32
1	27	32

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	44143×	body	80	nan
964.0ms	14865×	body	80	valid