Details

sample110.0ms

Algorithm

intervals

Results

39.0ms	847×	body	80	nan
11.0ms	205×	body	80	valid
7.0ms	22×	body	640	valid
3.0ms	4×	body	1280	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(* (- x 1.0) (log y))
5.2b	(log (- 1.0 y))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`fma-neg` `log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 114

Calls

4 calls:

28.0ms	(* (- z 1.0) (log (- 1.0 y)))
91.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
22.0ms	(* (- x 1.0) (log y))
6.0ms	(log (- 1.0 y))

series277.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (- z 1.0) (log (- 1.0 y)))
145.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
51.0ms	(* (- x 1.0) (log y))
42.0ms	(log (- 1.0 y))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	587	1089
1	2183	902
2	5001	886

prune345.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(* (- x 1.0) (log y))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
76×	`*-un-lft-identity`
67×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
31×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`unswap-sqr`
18×	`pow1`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod` `prod-exp`
9×	`div-exp` `add-log-exp`
8×	`flip3--` `log-pow` `flip--`
7×	`associate--l+`
6×	`pow-to-exp` `pow-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `fma-neg` `associate-r/` `pow-prod-down` `-commutative`
2×	`diff-log`
1×	`cbrt-undiv` `sum-log` `div-inv`

Counts

4 → 240

Calls

4 calls:

92.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
36.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
83.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
26.0ms	(* (- x 1.0) (log y))

series387.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
46.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
62.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
51.0ms	(* (- x 1.0) (log y))

simplify59.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1174	3396
1	5002	2459

prune816.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
24×	`log-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+l+`
18×	`cbrt-prod` `prod-diff`
12×	`associate-+r+`
7×	`pow1`
6×	`add-exp-log` `associate-*l/` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`expm1-log1p-u` `associate-*r/` `frac-add` `log1p-expm1-u`
3×	`pow1/3`
2×	`sub-neg` `log-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

23.0ms	(* (- x 1.0) (log (cbrt y)))
36.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series750.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- x 1.0) (log (cbrt y)))
279.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
180.0ms	(cbrt y)
175.0ms	(cbrt y)

simplify80.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	542	1129
1	2640	925
2	5002	878

prune742.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.2b	(fma (* 2 (log (cbrt y))) (- x 1.0) (* (- x 1.0) (log (cbrt y))))
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`cbrt-prod` `add-cube-cbrt` `log-prod`
7×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-*l/` `log-pow`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

23.0ms	(* (- x 1.0) (log (cbrt y)))
0.0ms	(fma (* 2 (log (cbrt y))) (- x 1.0) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series759.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- x 1.0) (log (cbrt y)))
296.0ms	(fma (* 2 (log (cbrt y))) (- x 1.0) (* (- x 1.0) (log (cbrt y))))
169.0ms	(cbrt y)
179.0ms	(cbrt y)

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	244	528
1	948	463
2	5001	439

prune447.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	23974×	body	80	nan
319.0ms	5867×	body	80	valid
228.0ms	750×	body	640	valid
155.0ms	259×	body	1280	valid
135.0ms	736×	body	320	valid
50.0ms	419×	body	160	valid