Details

sample154.0ms

Algorithm

intervals

Results

72.0ms	97×	body	1280	valid
36.0ms	22×	body	2560	valid
26.0ms	69×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	39×	body	80	valid
2.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

17.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series151.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify78.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune121.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
2.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
95.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series810.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (tan x) (tan eps))
223.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
100.0ms	(* (tan x) (tan eps))
389.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	559	2923
1	2054	2373
2	5001	2349

prune413.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.0b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
99.0ms	(+ (tan x) (tan eps))
100.0ms	(* (tan x) (tan eps))
312.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	367	754
1	1426	679
2	5001	679

prune297.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.0b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
16.0ms	(/ (* (tan x) (sin eps)) (cos eps))
14.0ms	(* (tan x) (sin eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan x) (tan eps))
104.0ms	(/ (* (tan x) (sin eps)) (cos eps))
73.0ms	(* (tan x) (sin eps))
317.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	350	661
1	1333	582
2	5001	581

prune298.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.8b

regimes153.0ms

Accuracy

87.9% (0.9b remaining)

Error of 15.2b against oracle of 14.3b and baseline of 21.7b

bsearch131.0ms

Steps

Iters	Range		Point
7	4.306367868598726e-53	1.341374174211449e-51	1.5672909055063217e-52
7	-2.4941919585295986e-29	-1.9547976034035862e-31	-1.7700780661170397e-29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	49
1	39	49

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3234×	body	1280	valid
1.1s	653×	body	2560	valid
791.0ms	1898×	body	640	valid
222.0ms	778×	body	320	valid
98.0ms	1115×	body	80	valid
58.0ms	322×	body	160	valid