Details

sample334.0ms

Algorithm

intervals

Results

264.0ms

3370×

body

valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down` `cube-prod`
22×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`sqrt-prod`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 172

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series86.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(pow (/ 1.0 (fabs x)) 3)
30.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify123.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	584	1144
1	3655	959
2	5003	912

prune669.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
98×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
13×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series89.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify108.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	535	1298
1	3321	1112
2	5001	972

prune911.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

1015×	`add-exp-log`
524×	`prod-exp`
523×	`div-exp`
202×	`times-frac`
194×	`pow-exp`
193×	`pow-to-exp`
161×	`associate-r`
134×	`add-sqr-sqrt`
121×	`add-cube-cbrt` `*-un-lft-identity`
85×	`unpow-prod-down` `cube-prod`
84×	`add-cbrt-cube`
70×	`1-exp`
34×	`cbrt-unprod`
26×	`cbrt-undiv`
25×	`cube-mult` `unpow3` `sqr-pow`
18×	`pow1`
14×	`associate-l`
13×	`swap-sqr`
7×	`div-inv`
6×	`frac-times` `associate-*l/`
4×	`associate-*r/` `pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `sqrt-prod`
2×	`*-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 526

Calls

4 calls:

124.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series229.0ms

Counts

4 → 10

Calls

4 calls:

177.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify95.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1957	6352
1	5001	5134

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
0.4b	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite616.0ms

Algorithm

rewrite-expression-head

Rules

2221×	`add-exp-log`
1261×	`prod-exp`
1037×	`div-exp`
386×	`pow-exp`
385×	`pow-to-exp`
162×	`times-frac`
153×	`add-cbrt-cube`
151×	`associate-r`
140×	`1-exp`
95×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
85×	`unpow-prod-down` `cube-prod`
78×	`frac-times`
75×	`cbrt-unprod`
50×	`associate-*l/`
43×	`cbrt-undiv`
34×	`associate-*r/`
25×	`cube-mult` `unpow3` `sqr-pow`
24×	`frac-add`
20×	`pow1`
9×	`pow-prod-down`
8×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod` `div-inv`
2×	`associate-l` `*-commutative` `rem-cube-cbrt`
1×	`cube-div` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 759

Calls

4 calls:

403.0ms	(* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
128.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series479.0ms

Counts

4 → 10

Calls

4 calls:

264.0ms	(* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
175.0ms	(* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
40.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify164.0ms

Algorithm

egg-herbie

Counts

769 → 769

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2764	13884
1	5001	12553

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes427.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	42
1	56	42

end0.0ms

sample7.2s

Algorithm

intervals

Results

6.0s

78267×

body

valid