Details

sample173.0ms

Algorithm

intervals

Results

74.0ms	1417×	body	80	nan
28.0ms	469×	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: 0.2b

localize16.0ms

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))

rewrite136.0ms

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))
81.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
37.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series385.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
172.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
116.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify60.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (49.0ms)

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

prune433.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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:

43.0ms	(* 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:

545.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
73.0ms	(fma (log (/ 1 a)) t b)
344.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify99.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (74.0ms)

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

prune824.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

520×	`add-exp-log`
271×	`div-exp`
210×	`prod-exp`
82×	`pow-exp`
38×	`add-cbrt-cube`
26×	`pow-to-exp`
20×	`1-exp`
17×	`cbrt-undiv`
16×	`cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-/r` `fma-udef` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 142

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)
77.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 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 (/ (cbrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series554.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (log (/ 1 a)) t b)
73.0ms	(fma (log (/ 1 a)) t b)
73.0ms	(fma (log (/ 1 a)) t b)
330.0ms	(/ (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 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 (/ (cbrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify108.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	1101	4774
1	3470	4002
2	5001	3747

prune485.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

2149×	`add-exp-log`
1164×	`prod-exp`
922×	`div-exp`
328×	`pow-exp`
161×	`1-exp`
104×	`pow-to-exp`
81×	`rec-exp` `add-cbrt-cube`
50×	`cbrt-unprod`
25×	`cbrt-undiv`
13×	`pow1` `associate-r`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-*r/`
6×	`pow-prod-down`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`associate-l` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 407

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)
283.0ms	(* (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 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 (/ (cbrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))

series569.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma (log (/ 1 a)) t b)
80.0ms	(fma (log (/ 1 a)) t b)
79.0ms	(fma (log (/ 1 a)) t b)
332.0ms	(* (* (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 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 (/ (cbrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))

simplify186.0ms

Algorithm

egg-herbie

Counts

419 → 419

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	2057	14986
1	5001	12868

prune552.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (1.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	39
1	34	39

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.2s	44143×	body	80	nan
893.0ms	14865×	body	80	valid