Details

sample34.0ms

Algorithm

intervals

Results

23.0ms

268×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(- (* b c) (* a d))
26.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
3.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
41.0ms	(- (* b c) (* a d))
87.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune183.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
15.3b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* b c) (* a d))
12.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
112.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune286.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
15.3b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
31.2b	(sqrt (+ (* c c) (* d d)))
31.2b	(sqrt (+ (* c c) (* d d)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`sqrt-div` `div-inv`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

15.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
11.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d))))
78.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify70.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	574	2907
1	2461	2677
2	5001	2540

prune414.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(- (* b c) (* a d))
0.5b	(/ 1 (+ (* c c) (* d d)))
25.9b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
6.0ms	(/ 1 (+ (* c c) (* d d)))
25.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* c c) (* d d))
40.0ms	(- (* b c) (* a d))
36.0ms	(/ 1 (+ (* c c) (* d d)))
85.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	384	857
1	1929	753
2	5002	724

prune223.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.7b

regimes131.0ms

Accuracy

0% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	14
1	20	14

end0.0ms

sample961.0ms

Algorithm

intervals

Results

738.0ms

8429×

body

valid