Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

276×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 28.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
27.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite44.0ms

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:

8.0ms	(+ (* c c) (* d d))
10.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* c c) (* d d))
35.0ms	(- (* b c) (* a d))
80.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

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

prune178.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 27.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.8b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite53.0ms

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:

8.0ms	(- (* b c) (* a d))
28.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b c) (* a d))
105.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
32.0ms	(sqrt (+ (* c c) (* d d)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

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

prune282.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.8b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
23.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b c) (* a d))
73.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
32.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	264	887
1	808	842
2	2357	837
3	5001	837

prune283.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.8b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.6b	(sqrt (+ (* c c) (* d d)))
29.6b	(sqrt (+ (* c c) (* d d)))

rewrite51.0ms

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:

8.0ms	(- (* b c) (* a d))
26.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b c) (* a d))
107.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
32.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify95.0ms

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

prune277.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.1b

regimes155.0ms

Accuracy

3.3% (2.8b remaining)

Error of 26.4b against oracle of 23.5b and baseline of 26.4b

bsearch40.0ms

Steps

Iters	Range		Point
9	1.4444100680103096e+82	2.0449168201690372e+88	2.0132411455167335e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	20
1	30	20
2	30	20

end0.0ms

sample586.0ms

Algorithm

intervals

Results

281.0ms

8506×

body

valid