Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
27.7b	(/ (+ (* a c) (* b 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`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
3.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
80.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify131.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune206.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.5b	(fma a c (* b d))
13.1b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

4.0ms	(/ 1 (* (hypot c d) 1))
22.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms	(fma a c (* b d))
3.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series383.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot c d) 1))
179.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
41.0ms	(fma a c (* b d))
112.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify50.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune297.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.5b	(fma a c (* b d))
13.1b	(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

6.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series270.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
42.0ms	(fma a c (* b d))
113.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify76.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune298.0ms

Filtered

98 candidates to 76 candidates (77.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ (fma a c (* b d)) (hypot c d))) (- (hypot c d)))
0.5b	(fma a c (* b d))
13.1b	(/ (fma a c (* b d)) (hypot c d))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

507×	`times-frac`
269×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
236×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
42×	`neg-mul-1`
33×	`associate-/l*`
24×	`div-inv`
13×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `fma-udef` `associate-/l/` `distribute-neg-frac`

Counts

3 → 396

Calls

3 calls:

22.0ms	(/ (- (/ (fma a c (* b d)) (hypot c d))) (- (hypot c d)))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series276.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (- (/ (fma a c (* b d)) (hypot c d))) (- (hypot c d)))
41.0ms	(fma a c (* b d))
116.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify127.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1308	6232
1	4916	5949
2	5002	5949

prune985.0ms

Filtered

405 candidates to 260 candidates (64.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

regimes234.0ms

Accuracy

15.4% (9.2b remaining)

Error of 14.9b against oracle of 5.7b and baseline of 16.5b

bsearch41.0ms

Steps

Iters	Range		Point
8	1.695796626129481e+71	2.2080787432878896e+74	2.1850720944349345e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	36	11
2	40	11
3	40	11

end0.0ms

sample519.0ms

Algorithm

intervals

Results

299.0ms

8440×

body

valid